was@form:~/sage/bsd_comp$ was@form:~/sage/bsd_comp$ Magma V2.11-1 Thu Jul 1 2004 16:44:49 on form [Seed = 3429432110] Type ? for help. Type -D to quit. Loading startup file "/home/was/magma/local/emacs.m" Loading "/home/was/magma/local/init.m" > Attach("bsd.m"); [PC] [PC] In file "/home/was/papers/bsd_comp/bsd.m", line 20, column [PC] 4: [PC] >> rE, LE := AnalyticRank(E); [PC] ^ [PC] User error: bad syntax >> Attach("bsd.m"); ^ Runtime error in 'Attach': Can't attach intrinsics of "bsd.m" > Attach("bsd.m"); > AllCurves(2,50); -3 fails Heegner since is -3 or -4. -4 fails Heegner since is -3 or -4. -7 fails because only divisible by 1 prime. -8 fails because only divisible by 1 prime. -11 fails because only divisible by 1 prime. -15 fails Heegner since not every prime dividing conductor splits -19 fails because only divisible by 1 prime. -20 fails Heegner since not every prime dividing conductor splits -23 fails because only divisible by 1 prime. Using Kolyvagin theorem on D = -24 Rounding error in index computation: 0.00110212061554193496704 Got bound = 10 in 0.59 seconds. ************************************** ** N = 11 i = 1 ** bound = 10 disc = -24 ************************************** -3 fails Heegner since is -3 or -4. -4 fails Heegner since is -3 or -4. -7 fails because only divisible by 1 prime. -8 fails because only divisible by 1 prime. -11 fails because only divisible by 1 prime. -15 fails Heegner since not every prime dividing conductor splits -19 fails because only divisible by 1 prime. -20 fails Heegner since is not coprime to conductor. -23 fails because only divisible by 1 prime. -24 fails Heegner since is not coprime to conductor. -31 fails because only divisible by 1 prime. -35 fails Heegner since is not coprime to conductor. -39 fails Heegner since not every prime dividing conductor splits -40 fails Heegner since is not coprime to conductor. -43 fails because only divisible by 1 prime. -47 fails because only divisible by 1 prime. -51 fails Heegner since not every prime dividing conductor splits -51 fails Heegner since not every prime dividing conductor splits -52 fails Heegner since is not coprime to conductor. Using Kolyvagin theorem on D = -55 Rounding error in index computation: 0.00061919726431369781494 Got bound = 6 in 1.02 seconds. ************************************** ** N = 14 i = 1 ** bound = 6 disc = -55 ************************************** -3 fails Heegner since is -3 or -4. -4 fails Heegner since is -3 or -4. -7 fails because only divisible by 1 prime. -8 fails because only divisible by 1 prime. -11 fails because only divisible by 1 prime. -15 fails Heegner since is not coprime to conductor. -19 fails because only divisible by 1 prime. -20 fails Heegner since is not coprime to conductor. -23 fails because only divisible by 1 prime. -24 fails Heegner since is not coprime to conductor. -31 fails because only divisible by 1 prime. -35 fails Heegner since is not coprime to conductor. -39 fails Heegner since is not coprime to conductor. -40 fails Heegner since is not coprime to conductor. -43 fails because only divisible by 1 prime. -47 fails because only divisible by 1 prime. -51 fails Heegner since is not coprime to conductor. -52 fails Heegner since not every prime dividing conductor splits -52 fails Heegner since not every prime dividing conductor splits -55 fails Heegner since is not coprime to conductor. Using Kolyvagin theorem on D = -56 Rounding error in index computation: 0.0005036164075 Got bound = 2 in 1.509 seconds. ************************************** ** N = 15 i = 1 ** bound = 2 disc = -56 ************************************** -3 fails Heegner since is -3 or -4. -4 fails Heegner since is -3 or -4. -7 fails because only divisible by 1 prime. -8 fails because only divisible by 1 prime. -11 fails because only divisible by 1 prime. Using Kolyvagin theorem on D = -15 Rounding error in index computation: 0.0006640590727 Got bound = 2 in 0.77 seconds. ************************************** ** N = 17 i = 1 ** bound = 2 disc = -15 ************************************** -3 fails Heegner since is -3 or -4. -4 fails Heegner since is -3 or -4. -7 fails because only divisible by 1 prime. -8 fails because only divisible by 1 prime. -11 fails because only divisible by 1 prime. Using Kolyvagin theorem on D = -15 Rounding error in index computation: 0.00023949332535 Got bound = 6 in 0.759 seconds. ************************************** ** N = 19 i = 1 ** bound = 6 disc = -15 ************************************** -3 fails Heegner since is -3 or -4. -4 fails Heegner since is -3 or -4. -7 fails because only divisible by 1 prime. -8 fails because only divisible by 1 prime. -11 fails because only divisible by 1 prime. -15 fails Heegner since is not coprime to conductor. -19 fails because only divisible by 1 prime. -20 fails Heegner since is not coprime to conductor. -23 fails because only divisible by 1 prime. -24 fails Heegner since is not coprime to conductor. -31 fails because only divisible by 1 prime. -35 fails Heegner since is not coprime to conductor. Using Kolyvagin theorem on D = -39 Rounding error in index computation: 0.000092768110334873199462 Got bound = 6 in 0.721 seconds. ************************************** ** N = 20 i = 1 ** bound = 6 disc = -39 ************************************** -3 fails Heegner since is -3 or -4. -4 fails Heegner since is -3 or -4. -7 fails because only divisible by 1 prime. -8 fails because only divisible by 1 prime. -11 fails because only divisible by 1 prime. -15 fails Heegner since is not coprime to conductor. -19 fails because only divisible by 1 prime. Using Kolyvagin theorem on D = -20 Rounding error in index computation: 0.00012855790555477142333 Got bound = 2 in 1 seconds. ************************************** ** N = 21 i = 1 ** bound = 2 disc = -20 ************************************** -3 fails Heegner since is -3 or -4. -4 fails Heegner since is -3 or -4. -7 fails because only divisible by 1 prime. -8 fails because only divisible by 1 prime. -11 fails because only divisible by 1 prime. -15 fails Heegner since is not coprime to conductor. -19 fails because only divisible by 1 prime. -20 fails Heegner since is not coprime to conductor. -23 fails because only divisible by 1 prime. -24 fails Heegner since is not coprime to conductor. -31 fails because only divisible by 1 prime. -35 fails Heegner since not every prime dividing conductor splits -39 fails Heegner since is not coprime to conductor. -40 fails Heegner since is not coprime to conductor. -43 fails because only divisible by 1 prime. -47 fails because only divisible by 1 prime. -51 fails Heegner since is not coprime to conductor. -52 fails Heegner since is not coprime to conductor. -55 fails Heegner since not every prime dividing conductor splits -56 fails Heegner since is not coprime to conductor. -59 fails because only divisible by 1 prime. -67 fails because only divisible by 1 prime. -68 fails Heegner since is not coprime to conductor. -71 fails because only divisible by 1 prime. -79 fails because only divisible by 1 prime. -83 fails because only divisible by 1 prime. -84 fails Heegner since is not coprime to conductor. -87 fails Heegner since is not coprime to conductor. -88 fails Heegner since is not coprime to conductor. -91 fails Heegner since not every prime dividing conductor splits -91 fails Heegner since not every prime dividing conductor splits Using Kolyvagin theorem on D = -95 Rounding error in index computation: 0.000091932713985443115234 Got bound = 2 in 1.23 seconds. ************************************** ** N = 24 i = 1 ** bound = 2 disc = -95 ************************************** -3 fails Heegner since is -3 or -4. -4 fails Heegner since is -3 or -4. -7 fails because only divisible by 1 prime. -8 fails because only divisible by 1 prime. -11 fails because only divisible by 1 prime. -15 fails Heegner since not every prime dividing conductor splits -19 fails because only divisible by 1 prime. -20 fails Heegner since is not coprime to conductor. -23 fails because only divisible by 1 prime. -24 fails Heegner since is not coprime to conductor. -31 fails because only divisible by 1 prime. -35 fails Heegner since not every prime dividing conductor splits -39 fails Heegner since is not coprime to conductor. -40 fails Heegner since is not coprime to conductor. -43 fails because only divisible by 1 prime. -47 fails because only divisible by 1 prime. -51 fails Heegner since not every prime dividing conductor splits -52 fails Heegner since is not coprime to conductor. Using Kolyvagin theorem on D = -55 Rounding error in index computation: 0.0007479637861 Got bound = 6 in 18.301 seconds. ************************************** ** N = 26 i = 1 ** bound = 6 disc = -55 ************************************** -3 fails Heegner since is -3 or -4. -4 fails Heegner since is -3 or -4. -7 fails because only divisible by 1 prime. -8 fails because only divisible by 1 prime. -11 fails because only divisible by 1 prime. -15 fails Heegner since not every prime dividing conductor splits -19 fails because only divisible by 1 prime. -20 fails Heegner since is not coprime to conductor. -23 fails because only divisible by 1 prime. -24 fails Heegner since is not coprime to conductor. -31 fails because only divisible by 1 prime. -35 fails Heegner since not every prime dividing conductor splits -39 fails Heegner since is not coprime to conductor. -40 fails Heegner since is not coprime to conductor. -43 fails because only divisible by 1 prime. -47 fails because only divisible by 1 prime. -51 fails Heegner since not every prime dividing conductor splits -52 fails Heegner since is not coprime to conductor. Using Kolyvagin theorem on D = -55 Rounding error in index computation: 0.00036697369068861007690 Got bound = 14 in 6.16 seconds. ************************************** ** N = 26 i = 2 ** bound = 14 disc = -55 ************************************** -3 fails Heegner since is -3 or -4. -4 fails Heegner since is -3 or -4. -7 fails because only divisible by 1 prime. -8 fails because only divisible by 1 prime. -11 fails because only divisible by 1 prime. -15 fails Heegner since is not coprime to conductor. -19 fails because only divisible by 1 prime. Using Kolyvagin theorem on D = -20 Rounding error in index computation: 0.00021349452435 Got bound = 6 in 0.61 seconds. ************************************** ** N = 27 i = 1 ** bound = 6 disc = -20 ************************************** -3 fails Heegner since is -3 or -4. -4 fails Heegner since is -3 or -4. -7 fails because only divisible by 1 prime. -8 fails because only divisible by 1 prime. -11 fails because only divisible by 1 prime. -15 fails Heegner since is not coprime to conductor. -19 fails because only divisible by 1 prime. -20 fails Heegner since is not coprime to conductor. -23 fails because only divisible by 1 prime. -24 fails Heegner since is not coprime to conductor. -31 fails because only divisible by 1 prime. -35 fails Heegner since is not coprime to conductor. -39 fails Heegner since is not coprime to conductor. -40 fails Heegner since is not coprime to conductor. -43 fails because only divisible by 1 prime. -47 fails because only divisible by 1 prime. -51 fails Heegner since is not coprime to conductor. -52 fails Heegner since is not coprime to conductor. -55 fails Heegner since is not coprime to conductor. -56 fails Heegner since is not coprime to conductor. -59 fails because only divisible by 1 prime. -67 fails because only divisible by 1 prime. -68 fails Heegner since is not coprime to conductor. -71 fails because only divisible by 1 prime. -79 fails because only divisible by 1 prime. -83 fails because only divisible by 1 prime. -84 fails Heegner since is not coprime to conductor. -87 fails Heegner since is not coprime to conductor. -88 fails Heegner since is not coprime to conductor. -91 fails Heegner since not every prime dividing conductor splits -91 fails Heegner since not every prime dividing conductor splits -95 fails Heegner since is not coprime to conductor. -103 fails because only divisible by 1 prime. -104 fails Heegner since is not coprime to conductor. -107 fails because only divisible by 1 prime. -111 fails Heegner since is not coprime to conductor. -115 fails Heegner since is not coprime to conductor. -116 fails Heegner since is not coprime to conductor. Using Kolyvagin theorem on D = -119 Rounding error in index computation: 0.0003334581851 Got bound = 6 in 1.371 seconds. ************************************** ** N = 30 i = 1 ** bound = 6 disc = -119 ************************************** -3 fails Heegner since is -3 or -4. -4 fails Heegner since is -3 or -4. -7 fails because only divisible by 1 prime. -8 fails because only divisible by 1 prime. -11 fails because only divisible by 1 prime. Using Kolyvagin theorem on D = -15 Rounding error in index computation: 0.0002732835710 Got bound = 2 in 0.619 seconds. ************************************** ** N = 32 i = 1 ** bound = 2 disc = -15 ************************************** -3 fails Heegner since is -3 or -4. -4 fails Heegner since is -3 or -4. -7 fails because only divisible by 1 prime. -8 fails because only divisible by 1 prime. -11 fails because only divisible by 1 prime. -15 fails Heegner since is not coprime to conductor. -19 fails because only divisible by 1 prime. -20 fails Heegner since not every prime dividing conductor splits -23 fails because only divisible by 1 prime. -24 fails Heegner since is not coprime to conductor. -31 fails because only divisible by 1 prime. Using Kolyvagin theorem on D = -35 Rounding error in index computation: 0.00054012518376111984252 Got bound = 2 in 0.939 seconds. ************************************** ** N = 33 i = 1 ** bound = 2 disc = -35 ************************************** -3 fails Heegner since is -3 or -4. -4 fails Heegner since is -3 or -4. -7 fails because only divisible by 1 prime. -8 fails because only divisible by 1 prime. -11 fails because only divisible by 1 prime. Using Kolyvagin theorem on D = -15 Rounding error in index computation: 0.0003257412463 Got bound = 6 in 0.74 seconds. ************************************** ** N = 34 i = 1 ** bound = 6 disc = -15 ************************************** -3 fails Heegner since is -3 or -4. -4 fails Heegner since is -3 or -4. -7 fails because only divisible by 1 prime. -8 fails because only divisible by 1 prime. -11 fails because only divisible by 1 prime. -15 fails Heegner since is not coprime to conductor. -19 fails because only divisible by 1 prime. -20 fails Heegner since is not coprime to conductor. -23 fails because only divisible by 1 prime. Using Kolyvagin theorem on D = -24 Rounding error in index computation: 0.000079252757132053375244 Got bound = 6 in 0.62 seconds. ************************************** ** N = 35 i = 1 ** bound = 6 disc = -24 ************************************** -3 fails Heegner since is -3 or -4. -4 fails Heegner since is -3 or -4. -7 fails because only divisible by 1 prime. -8 fails because only divisible by 1 prime. -11 fails because only divisible by 1 prime. -15 fails Heegner since is not coprime to conductor. -19 fails because only divisible by 1 prime. -20 fails Heegner since is not coprime to conductor. -23 fails because only divisible by 1 prime. -24 fails Heegner since is not coprime to conductor. -31 fails because only divisible by 1 prime. -35 fails Heegner since not every prime dividing conductor splits -39 fails Heegner since is not coprime to conductor. -40 fails Heegner since is not coprime to conductor. -43 fails because only divisible by 1 prime. -47 fails because only divisible by 1 prime. -51 fails Heegner since is not coprime to conductor. -52 fails Heegner since is not coprime to conductor. -55 fails Heegner since not every prime dividing conductor splits -56 fails Heegner since is not coprime to conductor. -59 fails because only divisible by 1 prime. -67 fails because only divisible by 1 prime. -68 fails Heegner since is not coprime to conductor. -71 fails because only divisible by 1 prime. -79 fails because only divisible by 1 prime. -83 fails because only divisible by 1 prime. -84 fails Heegner since is not coprime to conductor. -87 fails Heegner since is not coprime to conductor. -88 fails Heegner since is not coprime to conductor. -91 fails Heegner since not every prime dividing conductor splits -91 fails Heegner since not every prime dividing conductor splits Using Kolyvagin theorem on D = -95 Rounding error in index computation: 0.0016601886600 Got bound = 6 in 0.869 seconds. ************************************** ** N = 36 i = 1 ** bound = 6 disc = -95 ************************************** -3 fails Heegner since is -3 or -4. -4 fails Heegner since is -3 or -4. -7 fails because only divisible by 1 prime. -8 fails because only divisible by 1 prime. -11 fails because only divisible by 1 prime. -15 fails Heegner since not every prime dividing conductor splits -19 fails because only divisible by 1 prime. -20 fails Heegner since not every prime dividing conductor splits -23 fails because only divisible by 1 prime. -24 fails Heegner since not every prime dividing conductor splits -31 fails because only divisible by 1 prime. -35 fails Heegner since not every prime dividing conductor splits -39 fails Heegner since not every prime dividing conductor splits Using Kolyvagin theorem on D = -40 Rounding error in index computation: 0.0010977238416 Got bound = 2 in 0.349 seconds. ************************************** ** N = 37 i = 1 ** bound = 2 disc = -40 ************************************** -3 fails Heegner since is -3 or -4. -4 fails Heegner since is -3 or -4. -7 fails because only divisible by 1 prime. -8 fails because only divisible by 1 prime. -11 fails because only divisible by 1 prime. -15 fails Heegner since not every prime dividing conductor splits -19 fails because only divisible by 1 prime. -20 fails Heegner since not every prime dividing conductor splits -23 fails because only divisible by 1 prime. -24 fails Heegner since not every prime dividing conductor splits -31 fails because only divisible by 1 prime. -35 fails Heegner since not every prime dividing conductor splits -39 fails Heegner since not every prime dividing conductor splits Using Kolyvagin theorem on D = -40 Rounding error in index computation: 0.0018433257937 Got bound = 6 in 0.659 seconds. ************************************** ** N = 37 i = 2 ** bound = 6 disc = -40 ************************************** -3 fails Heegner since is -3 or -4. -4 fails Heegner since is -3 or -4. -7 fails because only divisible by 1 prime. -8 fails because only divisible by 1 prime. -11 fails because only divisible by 1 prime. Using Kolyvagin theorem on D = -15 Rounding error in index computation: 0.00050459615886211395263 Got bound = 6 in 5.539 seconds. ************************************** ** N = 38 i = 1 ** bound = 6 disc = -15 ************************************** -3 fails Heegner since is -3 or -4. -4 fails Heegner since is -3 or -4. -7 fails because only divisible by 1 prime. -8 fails because only divisible by 1 prime. -11 fails because only divisible by 1 prime. Using Kolyvagin theorem on D = -15 Rounding error in index computation: 0.000101315788924694061279 Got bound = 10 in 0.549 seconds. ************************************** ** N = 38 i = 2 ** bound = 10 disc = -15 ************************************** -3 fails Heegner since is -3 or -4. -4 fails Heegner since is -3 or -4. -7 fails because only divisible by 1 prime. -8 fails because only divisible by 1 prime. -11 fails because only divisible by 1 prime. -15 fails Heegner since is not coprime to conductor. -19 fails because only divisible by 1 prime. -20 fails Heegner since rank of twist is too big. -23 fails because only divisible by 1 prime. -24 fails Heegner since is not coprime to conductor. -31 fails because only divisible by 1 prime. Using Kolyvagin theorem on D = -35 Rounding error in index computation: 0.00037438515573740005493 Got bound = 2 in 0.92 seconds. ************************************** ** N = 39 i = 1 ** bound = 2 disc = -35 ************************************** -3 fails Heegner since is -3 or -4. -4 fails Heegner since is -3 or -4. -7 fails because only divisible by 1 prime. -8 fails because only divisible by 1 prime. -11 fails because only divisible by 1 prime. -15 fails Heegner since is not coprime to conductor. -19 fails because only divisible by 1 prime. -20 fails Heegner since is not coprime to conductor. -23 fails because only divisible by 1 prime. -24 fails Heegner since is not coprime to conductor. -31 fails because only divisible by 1 prime. -35 fails Heegner since is not coprime to conductor. Using Kolyvagin theorem on D = -39 Rounding error in index computation: 0.000102009624242782592773 Got bound = 2 in 0.881 seconds. ************************************** ** N = 40 i = 1 ** bound = 2 disc = -39 ************************************** -3 fails Heegner since is -3 or -4. -4 fails Heegner since is -3 or -4. -7 fails because only divisible by 1 prime. -8 fails because only divisible by 1 prime. -11 fails because only divisible by 1 prime. -15 fails Heegner since is not coprime to conductor. -19 fails because only divisible by 1 prime. -20 fails Heegner since is not coprime to conductor. -23 fails because only divisible by 1 prime. -24 fails Heegner since is not coprime to conductor. -31 fails because only divisible by 1 prime. -35 fails Heegner since is not coprime to conductor. -39 fails Heegner since is not coprime to conductor. -40 fails Heegner since is not coprime to conductor. -43 fails because only divisible by 1 prime. -47 fails because only divisible by 1 prime. -51 fails Heegner since is not coprime to conductor. -52 fails Heegner since is not coprime to conductor. -55 fails Heegner since not every prime dividing conductor splits -56 fails Heegner since is not coprime to conductor. -59 fails because only divisible by 1 prime. -67 fails because only divisible by 1 prime. -68 fails Heegner since is not coprime to conductor. -71 fails because only divisible by 1 prime. -79 fails because only divisible by 1 prime. -83 fails because only divisible by 1 prime. -84 fails Heegner since is not coprime to conductor. -87 fails Heegner since is not coprime to conductor. -88 fails Heegner since is not coprime to conductor. -91 fails Heegner since is not coprime to conductor. -95 fails Heegner since not every prime dividing conductor splits -103 fails because only divisible by 1 prime. -104 fails Heegner since is not coprime to conductor. -107 fails because only divisible by 1 prime. -111 fails Heegner since is not coprime to conductor. -115 fails Heegner since not every prime dividing conductor splits -115 fails Heegner since not every prime dividing conductor splits -116 fails Heegner since is not coprime to conductor. -119 fails Heegner since is not coprime to conductor. -120 fails Heegner since is not coprime to conductor. -123 fails Heegner since is not coprime to conductor. -127 fails because only divisible by 1 prime. -131 fails because only divisible by 1 prime. -132 fails Heegner since is not coprime to conductor. -136 fails Heegner since is not coprime to conductor. -139 fails because only divisible by 1 prime. Using Kolyvagin theorem on D = -143 Rounding error in index computation: 0.00112321600317955017089 Got bound = 2 in 1.46 seconds. ************************************** ** N = 42 i = 1 ** bound = 2 disc = -143 ************************************** -3 fails Heegner since is -3 or -4. -4 fails Heegner since is -3 or -4. -7 fails because only divisible by 1 prime. -8 fails because only divisible by 1 prime. -11 fails because only divisible by 1 prime. -15 fails Heegner since not every prime dividing conductor splits -19 fails because only divisible by 1 prime. Using Kolyvagin theorem on D = -20 Rounding error in index computation: 0.00115641951560974121093 Got bound = 2 in 0.359 seconds. ************************************** ** N = 43 i = 1 ** bound = 2 disc = -20 ************************************** -3 fails Heegner since is -3 or -4. -4 fails Heegner since is -3 or -4. -7 fails because only divisible by 1 prime. -8 fails because only divisible by 1 prime. -11 fails because only divisible by 1 prime. -15 fails Heegner since not every prime dividing conductor splits -19 fails because only divisible by 1 prime. -20 fails Heegner since is not coprime to conductor. -23 fails because only divisible by 1 prime. -24 fails Heegner since is not coprime to conductor. -31 fails because only divisible by 1 prime. -35 fails Heegner since not every prime dividing conductor splits Using Kolyvagin theorem on D = -39 Rounding error in index computation: 0.00061100069433450698852 Got bound = 6 in 0.631 seconds. ************************************** ** N = 44 i = 1 ** bound = 6 disc = -39 ************************************** -3 fails Heegner since is -3 or -4. -4 fails Heegner since is -3 or -4. -7 fails because only divisible by 1 prime. -8 fails because only divisible by 1 prime. -11 fails because only divisible by 1 prime. -15 fails Heegner since is not coprime to conductor. -19 fails because only divisible by 1 prime. -20 fails Heegner since is not coprime to conductor. -23 fails because only divisible by 1 prime. -24 fails Heegner since is not coprime to conductor. -31 fails because only divisible by 1 prime. -35 fails Heegner since is not coprime to conductor. -39 fails Heegner since is not coprime to conductor. -40 fails Heegner since is not coprime to conductor. -43 fails because only divisible by 1 prime. -47 fails because only divisible by 1 prime. -51 fails Heegner since is not coprime to conductor. -52 fails Heegner since not every prime dividing conductor splits -52 fails Heegner since not every prime dividing conductor splits -55 fails Heegner since is not coprime to conductor. Using Kolyvagin theorem on D = -56 Rounding error in index computation: 0.00008787773549 Got bound = 2 in 1.85 seconds. ************************************** ** N = 45 i = 1 ** bound = 2 disc = -56 ************************************** -3 fails Heegner since is -3 or -4. -4 fails Heegner since is -3 or -4. -7 fails because only divisible by 1 prime. -8 fails because only divisible by 1 prime. -11 fails because only divisible by 1 prime. Using Kolyvagin theorem on D = -15 Rounding error in index computation: 0.0003357324749 Got bound = 2 in 0.579 seconds. ************************************** ** N = 46 i = 1 ** bound = 2 disc = -15 ************************************** -3 fails Heegner since is -3 or -4. -4 fails Heegner since is -3 or -4. -7 fails because only divisible by 1 prime. -8 fails because only divisible by 1 prime. -11 fails because only divisible by 1 prime. -15 fails Heegner since is not coprime to conductor. -19 fails because only divisible by 1 prime. -20 fails Heegner since is not coprime to conductor. -23 fails because only divisible by 1 prime. -24 fails Heegner since is not coprime to conductor. -31 fails because only divisible by 1 prime. -35 fails Heegner since not every prime dividing conductor splits -39 fails Heegner since is not coprime to conductor. -40 fails Heegner since is not coprime to conductor. -43 fails because only divisible by 1 prime. -47 fails because only divisible by 1 prime. -51 fails Heegner since is not coprime to conductor. -52 fails Heegner since is not coprime to conductor. -55 fails Heegner since rank of twist is too big. -56 fails Heegner since is not coprime to conductor. -59 fails because only divisible by 1 prime. -67 fails because only divisible by 1 prime. -68 fails Heegner since is not coprime to conductor. -71 fails because only divisible by 1 prime. -79 fails because only divisible by 1 prime. -83 fails because only divisible by 1 prime. -84 fails Heegner since is not coprime to conductor. -87 fails Heegner since is not coprime to conductor. -88 fails Heegner since is not coprime to conductor. -91 fails Heegner since not every prime dividing conductor splits -91 fails Heegner since not every prime dividing conductor splits Using Kolyvagin theorem on D = -95 Rounding error in index computation: 0.0000084266066551208496093 Got bound = 2 in 1.619 seconds. ************************************** ** N = 48 i = 1 ** bound = 2 disc = -95 ************************************** -3 fails Heegner since is -3 or -4. -4 fails Heegner since is -3 or -4. -7 fails because only divisible by 1 prime. -8 fails because only divisible by 1 prime. -11 fails because only divisible by 1 prime. -15 fails Heegner since not every prime dividing conductor splits -19 fails because only divisible by 1 prime. Using Kolyvagin theorem on D = -20 Rounding error in index computation: 0.0005231406539 Got bound = 2 in 0.93 seconds. ************************************** ** N = 49 i = 1 ** bound = 2 disc = -20 ************************************** -3 fails Heegner since is -3 or -4. -4 fails Heegner since is -3 or -4. -7 fails because only divisible by 1 prime. -8 fails because only divisible by 1 prime. -11 fails because only divisible by 1 prime. -15 fails Heegner since is not coprime to conductor. -19 fails because only divisible by 1 prime. -20 fails Heegner since is not coprime to conductor. -23 fails because only divisible by 1 prime. -24 fails Heegner since is not coprime to conductor. -31 fails because only divisible by 1 prime. -35 fails Heegner since is not coprime to conductor. Using Kolyvagin theorem on D = -39 Rounding error in index computation: 0.0007601324468 Got bound = 6 in 2.761 seconds. ************************************** ** N = 50 i = 1 ** bound = 6 disc = -39 ************************************** -3 fails Heegner since is -3 or -4. -4 fails Heegner since is -3 or -4. -7 fails because only divisible by 1 prime. -8 fails because only divisible by 1 prime. -11 fails because only divisible by 1 prime. -15 fails Heegner since is not coprime to conductor. -19 fails because only divisible by 1 prime. -20 fails Heegner since is not coprime to conductor. -23 fails because only divisible by 1 prime. -24 fails Heegner since is not coprime to conductor. -31 fails because only divisible by 1 prime. -35 fails Heegner since is not coprime to conductor. Using Kolyvagin theorem on D = -39 Rounding error in index computation: 0.0019447179511189460754 Got bound = 10 in 2.429 seconds. ************************************** ** N = 50 i = 2 ** bound = 10 disc = -39 ************************************** >