3-coverings for elliptic curves of positive rank ================================================ 37 A 1 x^2*y + x^2*z + x*y^2 + 2*x*y*z + y*z^2 43 A 1: x^2*y - x^2*z + x*y^2 - y*z^2 53 A 1: x^2*y + x*y*z - x*z^2 + y^2*z + y*z^2 57 A 1: x^2*y - x*y^2 - 2*x*y*z + x*z^2 - y^2*z 58 A 1: x^2*y + x*y*z + x*z^2 - y^3 + y*z^2 61 A 1: x^2*y + x^2*z + x*y^2 + 3*x*y*z - y*z^2 65 A 1: x^2*y + x*y^2 - x*y*z - x*z^2 + y*z^2 65 A 2: x^2*z + x*y^2 + x*y*z + x*z^2 - y^3 - y^2*z - 3*y*z^2 77 A 1: 2*x^3 + x^2*y + x*z^2 - y^2*z 79 A 1: x^2*y + x^2*z + x*y^2 + 3*x*y*z + y*z^2 82 A 1: x^2*z + x*y^2 + x*y*z - y^3 + y*z^2 82 A 2: x^2*y + x^2*z + x*y*z - y^2*z + 4*y*z^2 + 5*z^3 83 A 1: x^3 - x^2*y + x^2*z + x*y^2 - x*y*z + y*z^2 88 A 1: x^2*y + 2*x*y*z + 2*x*z^2 + 2*y^2*z + y*z^2 89 A 1: x^2*z + x*y^2 - x*y*z - y^2*z - y*z^2 91 A 1: x^3 - x^2*z + x*y^2 + y*z^2 91 B 1: E[3] splits 91 B 2: E[3] splits 91 B 3: E[3] splits 92 B 1: x^3 - x*y^2 + y*z^2 + z^3 99 A 1: x^2*z + x*y^2 + x*y*z - y^3 + y^2*z + y*z^2 99 A 2: x^2*y - x^2*z - 3*x*y^2 + 5*x*y*z + y*z^2 (up to N = 100) 3-coverings for elliptic curves with nontrivial III[3] ====================================================== 182 B 3: E[3] splits 300 B 2: E[3] splits 378 A 3: E[3] splits 448 C 5: E[3] splits 448 C 6: E[3] splits 475 A 3: E[3] splits 510 G 3: E[3] splits 510 G 4: E[3] splits 546 D 3: E[3] splits 578 A 3: E[3] splits 578 A 4: E[3] splits 651 E 3: E[3] splits 660 D 3: E[3] splits 660 D 4: E[3] splits 681 B 1: 6*x^3 - 4*x^2*y - 3*x^2*z - 2*x*y^2 + x*y*z + 9*x*z^2 + y^3 + 4*y*z^2 - 3*z^3 x^3 - 4*x^2*y + 3*x^2*z + 6*x*y^2 + 5*x*y*z + 7*x*z^2 - y^3 - 4*y^2*z - 2*y*z^2 - 6*z^3 3*x^3 + 5*x^2*y - 5*x^2*z + 2*x*y^2 + 7*x*y*z + 3*x*z^2 - y^3 + y^2*z - y*z^2 + 4*z^3 3*x^3 + x^2*y + 3*x^2*z - 2*x*y^2 + 5*x*y*z + 9*x*z^2 - y^3 - 4*y^2*z - 7*y*z^2 + 3*z^3 681 B 2: 9*x^3 - 6*x^2*y + x^2*z - 9*x*y*z + x*z^2 + 3*y^3 + y^2*z + z^3 x^3 + 2*x^2*z + 4*x*y^2 - 3*x*y*z - 3*x*z^2 - y^3 - 7*y^2*z + 2*y*z^2 - 7*z^3 2*x^3 + 5*x^2*y + 4*x^2*z + 3*x*y^2 + x*y*z + 13*x*z^2 - y^3 + 2*y^2*z - 3*y*z^2 + 5*z^3 x^3 - 2*x^2*y + 5*x^2*z + 3*x*y^2 + 3*x*y*z + 10*x*z^2 + y^3 - y^2*z + 3*y*z^2 - 4*z^3 681 B 3: x^3 + 2*x^2*y + 3*x^2*z + 3*x*y^2 + 3*x*y*z - 5*x*z^2 - 7*y^3 + 7*y^2*z + 8*y*z^2 - 2*z^3 x^3 - 4*x^2*y - 8*x^2*z - 5*x*y^2 + 9*x*y*z - 3*x*z^2 + 6*y^3 + 2*y^2*z - 2*y*z^2 + z^3 3*x^3 + 5*x^2*y - 14*x^2*z + 2*x*y^2 + 7*x*y*z - 3*x*z^2 - y^3 + y^2*z + 5*y*z^2 + 4*z^3 3*x^3 + 2*x^2*y - 5*x^2*z - 6*x*y^2 + 9*x*y*z - 9*y^3 + 2*y*z^2 + z^3 681 B 4: x^3 - 13*x^2*y + 3*x^2*z - 2*x*y^2 + 3*x*y*z + 4*x*z^2 - 4*y^3 + y^2*z - 3*y*z^2 + z^3 3*x^3 + 4*x^2*y + 4*x^2*z + 4*x*y^2 - 9*x*y*z + 8*x*z^2 + 2*y^3 + y^2*z + y*z^2 + 5*z^3 7*x^3 - 3*x^2*y + 2*x^2*z + 10*x*y^2 - 9*x*y*z + 3*x*z^2 + y^3 - y^2*z + y*z^2 + 2*z^3 9*x^3 + 3*x^2*y + 4*x^2*z - 9*x*y*z + 4*x*z^2 + 3*y^3 + 4*y^2*z + z^3 702 P 3: E[3] splits 714 I 3: E[3] splits 798 E 5: E[3] splits 798 E 6: E[3] splits 910 E 3: E[3] splits 910 J 5: E[3] splits 910 J 6: E[3] splits 936 D 3: E[3] splits 1020 G 2: E[3] splits 1026 M 3: E[3] splits 1122 M 3: E[3] splits 1122 M 4: E[3] splits 1380 D 3: E[3] splits 1380 D 4: E[3] splits 1452 E 2: E[3] splits 1590 U 3: E[3] splits 1590 U 4: E[3] splits 1638 J 3: E[3] splits 1650 K 2: E[3] splits 1716 B 3: E[3] splits 1716 B 4: E[3] splits 1734 J 2: E[3] splits 1734L 2: E[3] splits 1806 G 3: E[3] splits 1872 S 3: E[3] splits 1890 J 3: E[3] splits 1890 R 2: E[3] splits 1890 W 3: E[3] splits 1913 B 1: x^3 + x^2*y + x^2*z + 5*x*y^2 - x*y*z + y^3 - y^2*z - z^3 x^3 - x^2*y + 2*x^2*z + x*y*z + 2*x*z^2 - y^3 - 2*y^2*z - 3*y*z^2 + 2*z^3 x^3 - 2*x^2*y + 2*x*y^2 + 3*x*y*z + 2*x*z^2 + y^3 - 3*y^2*z - z^3 x^3 + 2*x^2*y - 2*x^2*z + x*y^2 + 3*x*y*z - 2*x*z^2 + y^3 + y^2*z + y*z^2 - 2*z^3 1913 B 2: x^3 - 2*x^2*y - 2*x^2*z + 4*x*y^2 - x*y*z + x*z^2 - y^3 + 2*y^2*z - y*z^2 + z^3 x^3 + x^2*z + x*y^2 + 3*x*y*z - x*z^2 - y^3 + 2*y^2*z + 2*y*z^2 + z^3 x^3 - 2*x^2*y + 3*x*y*z + x*z^2 - y^3 - 3*y^2*z - 2*y*z^2 + z^3 x^3 + x^2*y + x^2*z - x*y^2 + 3*x*y*z + 2*x*z^2 - 2*y^3 - 2*y^2*z - y*z^2 + z^3 1953 G 3: E[3] splits 1995 F 3: E[3] splits 1998 L 3: E[3] splits 2006 E 1: 43*x^3 + 38*x^2*y + 22*x^2*z - 48*x*y^2 - 43*x*y*z + 65*x*z^2 + 11*y^3 - 5*y^2*z + 113*y*z^2 + 50*z^3 9*x^3 - 16*x^2*y - 27*x^2*z + 16*x*y^2 - 107*x*y*z + 92*x*z^2 + 45*y^3 - 5*y^2*z + 90*y*z^2 + 124*z^3 9*x^3 - 38*x^2*y - 75*x^2*z + 27*x*y^2 - 11*x*y*z - 91*x*z^2 - 34*y^3 - 22*y^2*z + 134*y*z^2 - 92*z^3 9*x^3 + 27*x^2*y + 16*x^2*z - 43*x*y^2 - 139*x*y*z - 32*x*z^2 + 92*y^3 - 15*y^2*z + 38*y*z^2 + 81*z^3 2220 C 2: E[3] splits 2310 T 3: E[3] splits 2310 T 6: E[3] splits 2310 T 7: (has #Sha_an = 36!) E[3] splits 2310 T 8: E[3] splits 2310U 3: E[3] splits 2310 U 4: E[3] splits 2346 K 2: E[3] splits 2352 T 3: E[3] splits 2352 T 4: E[3] splits 2352 X 2: E[3] splits 2366 D 1: E[3] splits 2418 B 3: E[3] splits 2429 B 1: 4*x^3 - 3*x^2*y + 3*x^2*z - 2*x*y^2 + 3*x*y*z + x*z^2 - y^3 - y^2*z + z^3 2*x^3 + x^2*y - x*y^2 + 3*x*y*z + 3*x*z^2 - y^3 - 2*y*z^2 + 2*z^3 x^3 + x^2*z - 5*x*y*z + 2*x*z^2 + 2*y^3 - y^2*z - 2*y*z^2 + 3*z^3 x^3 + x^2*y - x^2*z - 3*x*y^2 + 3*x*y*z + x*z^2 + 2*y^3 + y^2*z + 2*y*z^2 - 2*z^3 2429 B 2: x^3 + x^2*y - 3*x^2*z - x*y^2 + 9*x*y*z - x*z^2 + 6*y^3 - 3*y^2*z - 6*y*z^2 - 4*z^3 3*x^3 + 9*x^2*y - x^2*z + 4*x*y^2 + 9*x*y*z - x*z^2 + 5*y^3 + 7*y^2*z + y*z^2 - 2*z^3 x^3 - 2*x^2*y + 5*x^2*z - x*y^2 + 7*x*y*z - x*z^2 - 5*y^3 + 5*y^2*z + 6*y*z^2 + 2*z^3 4*x^3 + 5*x^2*y - 5*x^2*z + 6*x*y^2 + 3*x*y*z - x*z^2 - y^3 + 5*y^2*z - 2*y*z^2 + 3*z^3 2430 P 2: E[3] splits 2457 J 3: E[3] splits 2460 E 3: E[3] splits 2460 E 4: E[3] splits 2534 E 1: 8*x^3 - 30*x^2*y - 64*x^2*z + 4*x*y^2 - x*y*z + 18*x*z^2 - 14*y^3 - 19*y^2*z + 11*y*z^2 - 6*z^3 8*x^3 + 18*x^2*y + 4*x^2*z - 15*x*y^2 + 29*x*y*z + 20*x*z^2 + 10*y^3 + 22*y^2*z + 52*y*z^2 - 16*z^3 8*x^3 + 15*x^2*y + 3*x^2*z - 13*x*y^2 + 35*x*y*z + 20*x*z^2 + 12*y^3 + 33*y^2*z + 70*y*z^2 + z^3 8*x^3 + 6*x^2*y + 6*x^2*z - 7*x*y^2 - 23*x*y*z + 62*x*z^2 - 11*y^3 + 12*y^2*z - 61*y*z^2 + 12*z^3 2534 E 2: 32*x^3 - 14*x^2*y - 17*x^2*z + 14*x*y^2 - 91*x*y*z - 34*x*z^2 + 48*y^3 + 68*y^2*z + 34*y*z^2 + 32*z^3 15*x^3 + 40*x^2*y + 93*x^2*z - x*y^2 - 9*x*y*z + 60*x*z^2 + 10*y^3 - 28*y^2*z - 42*y*z^2 + 124*z^3 56*x^3 + 18*x^2*y - 96*x^2*z + 124*x*y^2 - 53*x*y*z + 34*x*z^2 + 16*y^3 + 14*y^2*z + 8*z^3 64*x^3 - 4*x^2*y + 60*x^2*z - 18*x*y^2 + 89*x*y*z + 55*x*z^2 + 16*y^3 + 6*y^2*z + 53*y*z^2 - 21*z^3 2534 E 3: 42*x^3 + 79*x^2*y - 66*x^2*z + 85*x*y^2 + 185*x*y*z + 232*x*z^2 - 36*y^3 - 37*y^2*z - 60*y*z^2 + 24*z^3 12*x^3 - 30*x^2*y - 94*x^2*z + 34*x*y^2 - 61*x*y*z + 348*x*z^2 + 32*y^3 + 29*y^2*z + 229*y*z^2 + 158*z^3 4*x^3 - 66*x^2*y + 55*x^2*z + 78*x*y^2 + 5*x*y*z - 36*x*z^2 - 448*y^3 + 256*y^2*z + 124*y*z^2 + 16*z^3 86*x^3 + 69*x^2*y - 62*x^2*z + 131*x*y^2 - 133*x*y*z - 60*x*z^2 + 52*y^3 + 64*y^2*z - 60*y*z^2 + 64*z^3 2534 E 4: 24*x^3 + 128*x^2*y + 66*x^2*z + 30*x*y^2 + x*y*z - 4*x*z^2 + 2*y^3 - 37*y^2*z + 29*y*z^2 + 26*z^3 38*x^3 + 17*x^2*y - 44*x^2*z - 88*x*y^2 + 91*x*y*z + 14*x*z^2 + 81*y^3 + 21*y^2*z - 18*y*z^2 - 16*z^3 10*x^3 + 49*x^2*y - 35*x^2*z + 47*x*y^2 - 5*x*y*z + 66*x*z^2 - 28*y^3 + 58*y^2*z - 54*y*z^2 + 64*z^3 21*x^3 - 17*x^2*y + 36*x^2*z - 18*x*y^2 + 25*x*y*z + 131*x*z^2 + 16*y^3 + 18*y^2*z + 106*y*z^2 + 4*z^3 2534 F 1: 2*x^3 + 2*x^2*y - 2*x^2*z + 4*x*y^2 - 5*x*y*z - x*z^2 + 3*y^3 + y^2*z - y*z^2 + 2*z^3 x^3 + x^2*y + 2*x^2*z + 6*x*y^2 - x*y*z + y^3 - 5*y^2*z + 2*y*z^2 - 2*z^3 4*x^3 + 4*x^2*y - 3*x^2*z - 4*x*y^2 + x*y*z + 2*x*z^2 + y^3 + 3*y*z^2 - z^3 x^3 + 3*x^2*y - 2*x^2*z - 7*x*y^2 + 3*x*y*z + x*z^2 + 8*y^3 + 4*y^2*z - z^3 2541 D 1: 70*x^3 - 2*x^2*y + 13*x^2*z + 26*x*y^2 - 8*x*y*z - 7*x*z^2 + y^3 - 14*y^2*z + 3*y*z^2 - z^3 x^3 + 58*x^2*y - 14*x^2*z + 16*x*y^2 + 6*x*y*z - x*z^2 + 11*y^3 + 24*y^2*z + 5*y*z^2 - z^3 9*x^3 - 7*x^2*y + 23*x^2*z + 12*x*y^2 + 6*x*y*z - 13*x*z^2 + y^3 - 13*y^2*z - 6*y*z^2 - 17*z^3 5*x^3 + 8*x^2*y + 4*x^2*z - 11*x*y^2 - 10*x*y*z + 12*x*z^2 + 5*y^3 - 27*y^2*z + 19*y*z^2 + 18*z^3 2550 O 2: E[3] splits 1590 C 3: E[3] splits 2601 H 1: 2*x^3 + 5*x^2*y + 4*x^2*z + 19*x*y^2 - 13*x*y*z - 6*x*z^2 - 35*y^3 - 29*y^2*z + 6*y*z^2 - 3*z^3 x^3 - 11*x^2*y - 11*x^2*z - 19*x*y^2 + 33*x*y*z - 11*x*z^2 + 5*y^3 - y^2*z -y*z^2 + 6*z^3 x^3 + x^2*y + 15*x^2*z + x*y^2 + 7*x*y*z - 30*x*z^2 + 3*y^3 + 11*y^2*z - 62*y*z^2 + 23*z^3 -3*x^3 - 6*x^2*y - 6*x^2*z + 30*x*y^2 + 9*x*y*z + 13*x*z^2 + 18*y^3 + 3*y^2*z + 3*y*z^2 + z^3 2601 H 2: 17*x^3 - 23*x^2*y - 3*x^2*z + 13*x*y^2 + 5*x*y*z + 12*x*z^2 + 5*y^3 + 19*y^2*z - 20*y*z^2 + 5*z^3 6*x^3 + 3*x^2*y + 2*x^2*z + 27*x*y^2 + 27*x*y*z + 5*x*z^2 + 9*y^3 + 6*y^2*z + 36*y*z^2 + 2*z^3 10*x^3 + 10*x^2*y - 7*x^2*z + 5*x*y^2 + 41*x*y*z + 11*x*z^2 - y^3 - 9*y^2*z + 18*y*z^2 - 17*z^3 x^3 + x^2*y + 18*x^2*z + 34*x*y^2 - 9*x*y*z - 6*x*z^2 + 3*y^3 + 3*y^2*z + 9*z^3 2670 E 3: E[3] splits 2670 E 4: E[3] splits 2674 B 1: 4*x^3 - 2*x^2*y - 5*x*y^2 - 11*x*y*z - x*z^2 + 7*y^3 + y^2*z + 3*y*z^2 + 2*z^3 3*x^3 - 5*x^2*y + 2*x^2*z - 13*x*y^2 - x*y*z + 2*x*z^2 - 4*y^3 - 7*y^2*z - 6*y*z^2 + z^3 4*x^3 - 2*x^2*z - 7*x*y^2 - 9*x*y*z + x*z^2 + 5*y^3 + 2*y^2*z + 4*y*z^2 + 3*z^3 16*x^3 - 11*x^2*y - 9*x^2*z + 10*x*y^2 - 5*x*y*z - x*z^2 + y^3 + 2*y^2*z + z^3 2674 B 2: 3*x^3 + 3*x^2*y - 17*x^2*z - x*y^2 + 19*x*y*z - 22*x*z^2 + 2*y^3 - 5*y^2*z - 12*y*z^2 - 28*z^3 2*x^3 + x^2*y - 17*x^2*z + 3*x*y^2 - 3*x*y*z + 8*x*z^2 + y^3 - 24*y^2*z - 2*y*z^2 - z^3 3*x^3 + 11*x^2*y + x^2*z - 3*x*y^2 - 7*x*y*z + 6*x*z^2 + 2*y^3 - 13*y^2*z + 24*y*z^2 + 4*z^3 20*x^3 + 12*x^2*y - 26*x^2*z + 25*x*y^2 + 7*x*y*z + 9*x*z^2 - y^3 + 2*y^2*z + z^3 2700 R 2: E[3] splits 2709 B 3: E[3] splits 2710 C 1: x^3 - 10*x^2*y + 6*x^2*z - 9*x*y^2 + 3*x*y*z + 4*x*z^2 - 2*y^3 - y^2*z - 31*y*z^2 + 17*z^3 18*x^3 - 7*x^2*y - 16*x^2*z + 12*x*y^2 - 7*x*y*z - 4*x*z^2 - 3*y^3 - 11*y^2*z + 9*y*z^2 - 2*z^3 4*x^3 + 5*x^2*y + 5*x^2*z + 10*x*y^2 + 19*x*y*z - 7*x*z^2 - 4*y^3 + 26*y^2*z + 7*y*z^2 + 5*z^3 38*x^3 - 13*x^2*y - 4*x^2*z - 9*x*y^2 - 3*x*y*z + 12*x*z^2 - y^3 - y^2*z - 9*y*z^2 - 2*z^3 2718 D 1: 51*x^3 - 118*x^2*y + 59*x^2*z - 24*x*y^2 - 107*x*y*z + 118*x*z^2 + 135*y^3 + 75*y^2*z + 86*y*z^2 + 68*z^3 68*x^3 - 59*x^2*y - 16*x^2*z + 59*x*y^2 + 225*x*y*z + 16*x*z^2 - 51*y^3 - 59*y^2*z + 59*y*z^2 + 136*z^3 33*x^3 - 169*x^2*y + 110*x^2*z + 62*x*y^2 + 27*x*y*z - 8*x*z^2 - 178*y^3 - 8*y^2*z + 67*y*z^2 + 17*z^3 10*x^3 + 188*x^2*y - 169*x^2*z + 142*x*y^2 - 129*x*y*z + 8*x*z^2 + 126*y^3 - 35*y^2*z - 59*y*z^2 - 17*z^3 2730 P 5: E[3] splits 2730 P 6: E[3] splits 2768 C 1: 2*x^3 + x^2*y - 2*x^2*z - 2*x*y^2 + 2*x*y*z + y^3 + 2*y*z^2 - 2*z^3 5*x^3 - 3*x^2*y + x*y^2 - 2*x*y*z - x*z^2 + y^3 + 2*y^2*z + y*z^2 + z^3 x^3 + x^2*y + 5*x*z^2 - y^3 + y^2*z - 2*y*z^2 - z^3 2*x^3 + x^2*y + 2*x^2*z - 2*x*y*z - y^3 - 2*y^2*z - 2*z^3 2768 C 2: 2*x^3 + 2*x^2*y + 4*x*y*z + x*z^2 + y^3 + 2*y^2*z + y*z^2 - z^3 x^3 - x^2*y + 2*x*y^2 + 2*x*y*z - 2*x*z^2 - y^3 + 2*y^2*z + 3*y*z^2 + 2*z^3 x^3 + 2*x^2*y + x*y^2 - 4*x*y*z + 4*x*z^2 - y^3 + y^2*z - y*z^2 - z^3 x^3 + x^2*y + x*y^2 - 4*x*y*z - x*z^2 - 2*y^3 - 3*y^2*z - z^3 2849 A 1: 20*x^3 + x^2*y - 9*x^2*z - 31*x*y^2 + 15*x*y*z + 3*x*z^2 + 20*y^3 + 2*y^2*z + 4*y*z^2 - z^3 x^3 + 6*x^2*y + x^2*z + 15*x*y^2 - 5*x*y*z + 29*x*z^2 + 2*y^3 - y^2*z - 5*z^3 4*x^3 + 13*x^2*y + 11*x^2*z + 2*x*y^2 - 7*x*y*z + 5*x*z^2 + 9*y^3 - 11*y^2*z - y*z^2 + 8*z^3 x^3 - 3*x^2*y + 4*x^2*z + 7*x*y^2 + 11*x*y*z + 4*x*z^2 + 25*y^3 - 32*y^2*z + 36*y*z^2 - 19*z^3 2849 A 2: 8*x^3 - 31*x^2*y + 17*x^2*z + 81*x*y^2 + x*y*z + 11*x*z^2 + 31*y^3 - 17*y^2*z + 6*y*z^2 - 2*z^3 2*x^3 + x^2*y - x^2*z - 7*x*y^2 - 39*x*y*z + 23*x*z^2 + 14*y^3 - 21*y^2*z + 72*y*z^2 + 89*z^3 10*x^3 + 13*x^2*y + 28*x^2*z + 39*x*y^2 + 13*x*y*z + 11*x*z^2 + 10*y^3 - 16*y^2*z + 3*y*z^2 - 14*z^3 10*x^3 + 29*x^2*z + 5*x*y^2 + 43*x*y*z + 13*x*z^2 + 13*y^3 - 9*y^2*z + 37*y*z^2 - 31*z^3 2932 A 1: x^3 + x^2*y + x^2*z - 3*x*y^2 + 4*x*y*z + 3*x*z^2 + 2*y^3 - 2*y^2*z + 6*y*z^2 - 2*z^3 x^3 - 4*x^2*y + 2*x*y*z + 2*x*z^2 - y^3 - 3*y^2*z - 7*y*z^2 - z^3 x^3 + 3*x^2*y + 2*x^2*z + 7*x*y^2 + 2*x*y*z + 2*x*z^2 + y^3 - 2*y^2*z - 2*z^3 x^3 - 2*x*y^2 + 2*x*y*z + 4*x*z^2 - 2*y^3 + 2*y^2*z - 6*y*z^2 + 4*z^3 2932 A 2: 3*x^3 + 3*x^2*y + x^2*z - x*y^2 - 6*x*y*z - x*z^2 + y^3 - y^2*z + y*z^2 + 2*z^3 x^3 - 2*x^2*y + x^2*z - 2*x*y^2 + 4*x*y*z + x*z^2 - y^3 - 2*y^2*z - 4*y*z^2 + 3*z^3 2*x^3 - 4*x^2*y - 4*x^2*z - 4*x*y*z - 2*x*z^2 - y^3 + y^2*z + y*z^2 - 2*z^3 4*x^3 - x^2*y - 3*x*y^2 - 6*x*y*z - y^3 - y^2*z - 3*y*z^2 - 2*z^3 2955 B 1: 22*x^3 + 4*x^2*y + 3*x^2*z - 6*x*y^2 + 3*x*y*z + 5*x*z^2 + 3*y^3 + 5*y*z^2 - 3*z^3 2*x^3 - 6*x^2*y - 7*x^2*z + 6*x*y^2 - 3*x*y*z - 3*x*z^2 - 5*y^3 - 14*y^2*z + 3*y*z^2 - 9*z^3 6*x^3 + 3*x^2*y + 2*x^2*z - 3*x*y^2 + 13*x*y*z + 5*x*z^2 - 9*y^3 + 12*y^2*z - 8*y*z^2 + 4*z^3 x^3 + 3*x^2*y - x*y^2 + 7*x*y*z + 9*y^3 + 20*y^2*z + 31*y*z^2 - 11*z^3 2955 B 2: 49*x^3 - 26*x^2*y - 44*x^2*z + 7*x*y^2 - 13*x*y*z - 24*x*z^2 - 3*y^3 - 6*y^2*z + 3*y*z^2 - 3*z^3 12*x^3 - 7*x^2*y - 19*x^2*z + 6*x*y^2 - 23*x*y*z + x*z^2 - 9*y^3 - 3*y^2*z + 18*y*z^2 - 9*z^3 15*x^3 - x^2*y - 4*x^2*z + 2*x*y^2 - 31*x*y*z - 21*x*z^2 + 2*y^3 + 5*y^2*z + y*z^2 + 37*z^3 9*x^3 + 35*x^2*y + 15*x^2*z - 24*x*y^2 - 21*x*y*z + 16*y^3 - 11*y^2*z + y*z^2 + 3*z^3 2955 B 3: 15*x^3 + 49*x^2*y - 6*x^2*z - 2*x*y^2 + 53*x*y*z + y^3 + 13*y^2*z + 60*y*z^2 - 27*z^3 4*x^3 + 11*x^2*y - 24*x^2*z + 31*x*y^2 + 31*x*y*z + 65*x*z^2 - 3*y^3 + 16*y^2*z + 5*y*z^2 + 45*z^3 6*x^3 + 2*x^2*y + 11*x^2*z - 2*x*y^2 - 61*x*y*z + 25*x*z^2 - 15*y^3 + 4*y^2*z - 51*y*z^2 - 97*z^3 11*x^3 - 27*x^2*y + 26*x^2*z - 20*x*y^2 + 13*x*y*z + 27*x*z^2 - 9*y^3 - 33*y^2*z - 33*y*z^2 + 36*z^3 2955 B 4: x^3 - 10*x^2*y - 3*x^2*z - 11*x*y^2 - 11*x*y*z + 15*x*z^2 + 9*y^3 + 23*y^2*z - 48*y*z^2 - 28*z^3 5*x^3 - 8*x^2*y - 4*x^2*z + 27*x*y^2 - 47*x*y*z - 4*x*z^2 + 39*y^3 + 5*y^2*z - 7*y*z^2 + 2*z^3 60*x^3 - 23*x^2*y - 42*x^2*z - 16*x*y^2 - 15*x*y*z - 4*x*z^2 - 8*y^3 - 3*y^2*z + 7*y*z^2 - z^3 3*x^3 - 10*x^2*y + 10*x^2*z + 12*x*y^2 + 33*x*y*z - 32*y^3 - y^2*z + 21*y*z^2 + 3*z^3 2982 J 3: E[3] splits 2982 J 4: E[3] splits 2992 K 2: E[3] splits 3054 A 1: 10*x^3 + x^2*y + 3*x^2*z + 2*x*y^2 + x*y*z - 3*x*z^2 - y^3 + 2*y^2*z + z^3 2*x^3 + 3*x^2*y - 3*x^2*z - 6*x*y^2 + x*y*z + x*z^2 + 4*y^3 - 2*y^2*z + 5*y*z^2 - z^3 2*x^3 + 3*x^2*y - x^2*z + 3*x*y^2 - 7*x*y*z + 6*x*z^2 - y^3 - 3*y^2*z + 4*y*z^2 - 4*z^3 7*x^3 - 6*x^2*z - x*y*z - 2*x*z^2 - y^3 - 2*y^2*z + 2*y*z^2 - z^3 3054 A 2: x^3 + 2*x^2*y + 2*x^2*z + 4*x*y^2 - 9*x*y*z - x*z^2 + 25*y^3 + 9*y^2*z - 9*y*z^2 + 2*z^3 2*x^3 - 6*x^2*y + x^2*z - 6*x*y^2 + 9*x*y*z + x*z^2 - 4*y^3 - 7*y^2*z - 8*y*z^2 + 3*z^3 4*x^3 + x^2*y + 4*x^2*z + x*y^2 + 13*x*y*z - 4*x*z^2 + 3*y^3 - 2*y^2*z + 3*y*z^2 - 8*z^3 25*x^3 + 8*x^2*y + 20*x^2*z + 2*x*y^2 - 7*x*y*z - 6*x*z^2 + y^3 + 2*y^2*z - 2*y*z^2 + z^3 3054 A 3: 9*x^3 - 24*x^2*z + 6*x*y^2 + x*y*z - 7*x*z^2 + y^3 - 19*y^2*z + 11*y*z^2 - 2*z^3 4*x^3 - 11*x^2*y - x^2*z - 10*x*y^2 + 13*x*y*z + 7*x*z^2 - 4*y^3 - 10*y^2*z - 27*y*z^2 + 3*z^3 12*x^3 + 23*x^2*y - 8*x^2*z + 9*x*y^2 + 3*x*y*z + 24*x*z^2 - 5*y^3 - 7*y^2*z - 9*y*z^2 - 6*z^3 3*x^3 + 8*x^2*y - 7*x^2*z + 9*x*y^2 + 13*x*y*z + x*z^2 - 8*y^3 + 22*y^2*z - 16*y*z^2 + 20*z^3 3054 A 4: 4*x^3 - 5*x^2*y - 3*x^2*z + 12*x*y^2 - 11*x*y*z - 3*x*z^2 + y^3 + 4*y^2*z + 3*z^3 x^3 + 5*x^2*y + x^2*z - x*y^2 - 7*x*y*z + 11*x*z^2 - 4*y^3 + 6*y^2*z - 8*y*z^2 - 8*z^3 2*x^3 + 9*x^2*y + 3*x^2*z - 18*x*y^2 + x*y*z + 5*x*z^2 + 4*y^3 - 2*y^2*z + 7*y*z^2 + 3*z^3 4*x^3 - 14*x^2*y - 3*x^2*z + 8*x*y^2 - 11*x*y*z - 4*x*z^2 - 8*y^3 + y^2*z + 5*y*z^2 - z^3 3094 H 3: E[3] splits 3294 K 3: E[3] splits 3300 O 2: E[3] splits 3306 B 1: 6*x^3 - 6*x^2*y + 2*x^2*z + 3*x*y^2 - 17*x*y*z + x*z^2 - 9*y^3 + 7*y^2*z - 5*y*z^2 - 4*z^3 2*x^3 - 12*x^2*y - 4*x^2*z - x*y^2 + 13*x*y*z + 5*x*z^2 - 4*y^3 - 13*y^2*z - 21*y*z^2 - z^3 2*x^3 + x^2*y - 15*x*y*z + 26*x*z^2 - 2*y^3 + 2*y^2*z - 5*y*z^2 - 46*z^3 x^3 - 7*x^2*y + 17*x^2*z - x*y^2 + 11*x*y*z - 8*x*z^2 - 2*y^3 - y^2*z + 4*y*z^2 + 14*z^3 3450 M 2: E[3] splits 3450 AA 2: E[3] splits 3510 S 3: E[3] splits 3536 H 1: 32*x^3 - 22*x^2*y + x^2*z - 24*x*y^2 - 56*x*y*z + 18*x*z^2 + 2*y^3 + 21*y^2*z - 42*y*z^2 + z^3 34*x^3 + 35*x^2*y + 41*x^2*z - 16*x*y^2 - 12*x*y*z + 54*x*z^2 - y^3 + 3*y^2*z + 40*y*z^2 - 6*z^3 4*x^3 + 18*x^2*y - 28*x^2*z - 4*x*y^2 + 30*x*y*z + 90*x*z^2 - 9*y^3 + 22*y^2*z - 53*y*z^2 - 12*z^3 47*x^3 + 4*x^2*y + 19*x^2*z - 37*x*y^2 + 18*x*y*z - x*z^2 - 16*y^3 - 33*y^2*z - 26*y*z^2 + 3*z^3 3536 H 2: 236*x^3 + 76*x^2*y + 190*x^2*z + 30*x*y^2 - 14*x*y*z - 36*x*z^2 + 12*y^3 + 37*y^2*z + 2*y*z^2 + z^3 88*x^3 + 48*x^2*y + 36*x^2*z + 74*x*y^2 - 66*x*y*z - 23*x*z^2 + 42*y^3 + 46*y^2*z - 23*y*z^2 + 6*z^3 24*x^3 + 56*x^2*y + 10*x^2*z - 20*x*y^2 - 46*x*y*z + 46*x*z^2 - 64*y^3 - 31*y^2*z - 54*y*z^2 - 23*z^3 306*x^3 - 30*x^2*y + 26*x^2*z - 56*x*y^2 + 66*x*y*z + 41*x*z^2 + 12*y^3 + 23*y*z^2 - 6*z^3 3540 G 2: E[3] splits 3555 E 1: x^3 - 2*x^2*y + 7*x^2*z - x*y^2 + 4*x*y*z - x*z^2 - y^3 + 3*y*z^2 + 5*z^3 3*x^3 - 10*x^2*y + 4*x^2*z - 2*x*y^2 + 6*x*y*z - x*z^2 - y^3 - y^2*z - 2*y*z^2 + z^3 x^3 - x^2*y + 2*x^2*z + 4*x*y*z + 7*x*z^2 + y^3 + 5*y*z^2 - 11*z^3 x^3 + 3*x^2*y - 2*x^2*z - 3*x*y^2 + 2*x*y*z + 3*x*z^2 + y^3 + y^2*z + 6*y*z^2 - 3*z^3 3555 E 2: 3*x^3 + 2*x^2*y - 2*x^2*z - x*y^2 + 12*x*y*z + 13*x*z^2 - y^3 - 10*y^2*z + y*z^2 + 7*z^3 x^3 + 5*x^2*y + 10*x^2*z - 6*x*y^2 - 4*x*y*z + 4*x*z^2 - 5*y^3 - 3*y^2*z - 10*y*z^2 - z^3 10*x^3 - 13*x^2*y - 5*x^2*z + x*y^2 - 12*x*y*z + 5*x*z^2 + 3*y^3 - y^2*z - 2*y*z^2 - z^3 x^3 - 2*x^2*y - 7*x^2*z + 13*x*y^2 - 4*x*y*z + 6*x*z^2 - y^3 - y^2*z + 9*y*z^2 - 5*z^3 3564 F 2: E[3] splits 3605 C 3: E[3] splits 3630 M 2: E[3] splits 3630 V 2: E[3] splits 3712 J 1: x^3 + x^2*y + 3*x^2*z + 2*x*y^2 - 10*x*y*z + 8*x*z^2 - 3*y^3 + 2*y^2*z - 5*y*z^2 - 8*z^3 7*x^3 + 6*x^2*y + 8*x^2*z - 2*x*y^2 + 2*x*y*z + 10*x*z^2 - 2*y^3 - y^2*z - 4*y*z^2 + 2*z^3 x^3 + 2*x^2*y - 4*x^2*z + 4*x*y^2 + 6*x*y*z + 7*x*z^2 - 5*y^3 - 6*y*z^2 + 2*z^3 x^3 - 5*x^2*y - 5*x^2*z - 5*x*y^2 - 8*x*y*z - x*z^2 - 7*y^3 + 3*y*z^2 - 2*z^3 3712 J 2: 2*x^3 + 2*x^2*y - 6*x^2*z + 3*x*y^2 - 8*x*y*z - 2*x*z^2 - y^3 - 11*y^2*z + 4*y*z^2 - 2*z^3 x^3 - 3*x^2*y - x^2*z - 7*x*y^2 - 10*x*y*z - x*z^2 - 7*y^3 - y^2*z - 7*y*z^2 - 5*z^3 4*x^3 + 7*x^2*y + 5*x^2*z + 10*x*y^2 - 2*y^3 - 6*y^2*z - 2*y*z^2 - 2*z^3 x^3 + 2*x^2*y + 3*x^2*z + 6*x*y^2 + 4*x*y*z + 13*x*z^2 - 2*y^3 - 2*y*z^2 + 3*z^3 3850 E 2: E[3] splits 3850 Y 2: E[3] splits 3879 E 1: 13*x^3 + 8*x^2*y - 8*x^2*z - 22*x*y^2 + 6*x*y*z + 7*x*z^2 + 7*y^3 - y^2*z + 10*y*z^2 - 3*z^3 x^3 + 14*x^2*y + 27*x^2*z + 6*x*y^2 + 10*x*y*z + 6*y^3 + 9*y^2*z - 7*y*z^2 + z^3 9*x^3 + 3*x^2*z + 3*x*y^2 + 24*x*y*z + x*z^2 - 9*y^3 + 6*y*z^2 + 6*z^3 x^3 + 7*x^2*y - 18*x^2*z + 4*x*y^2 - 8*x*y*z + 9*x*z^2 + 9*y^3 - 25*y^2*z + y*z^2 - z^3 3879 E 2: 21*x^3 - 56*x^2*y + 46*x^2*z - x*y^2 - 24*x*y*z + x*z^2 + 7*y^3 + 14*y^2*z - y*z^2 - 11*z^3 12*x^3 + 27*x^2*y + 12*x^2*z + 3*x*y^2 + 30*x*y*z - 26*x*z^2 - 9*y^3 - 27*y^2*z - 12*y*z^2 + 9*z^3 3*x^3 - 49*x^2*y + 5*x^2*z - 58*x*y*z + 5*x*z^2 + 3*y^3 - 15*y^2*z + 20*y*z^2 - z^3 11*x^3 - 21*x^2*y - 35*x^2*z - 6*x*y^2 + 68*x*y*z - 8*x*z^2 - y^3 + 19*y^2*z - 8*y*z^2 - z^3 3933 A 1: x^3 - 3*x^2*y - 2*x^2*z - 9*x*y^2 - 23*x*y*z - 3*x*z^2 - 16*y^3 + 4*y^2*z - 15*y*z^2 - 21*z^3 2*x^3 + 25*x^2*y - 13*x^2*z + 3*x*y^2 - x*y*z + x*z^2 + 3*y^3 + 9*y^2*z + 4*y*z^2 - 5*z^3 9*x^3 - 12*x^2*y - 9*x^2*z + 12*x*y^2 + 27*x*y*z - 3*x*z^2 + y^3 - 19*y^2*z - 11*y*z^2 - 6*z^3 3*x^3 + 7*x^2*y + 41*x^2*z - x*y^2 - 13*x*y*z - 22*x*z^2 + y^3 + 3*y^2*z - 12*y*z^2 + 17*z^3 3933 A 2: 19*x^3 + 3*x^2*y - 4*x^2*z + 24*x*y^2 + 9*x*y*z - 4*x*z^2 - 9*y^3 + 15*y^2*z + z^3 9*x^3 - 13*x^2*y - x^2*z + 15*x*y^2 - 9*x*y*z - 15*x*z^2 - 9*y^3 - 9*y^2*z + 3*y*z^2 - 6*z^3 3*x^3 + 13*x^2*y + 8*x^2*z + 7*x*y^2 - 13*x*y*z - 9*x*z^2 + 4*y^3 - 13*y^2*z - 3*y*z^2 + 21*z^3 x^3 + 15*x^2*y + 8*x^2*z + 9*x*y^2 + 5*x*y*z + 2*y^3 - 10*y^2*z + 15*y*z^2 + 12*z^3 3933 A 3: 2*x^3 + 5*x^2*y + 11*x^2*z - 15*x*y^2 - 5*x*y*z - 17*x*z^2 - 9*y^3 - 15*y^2*z + 2*y*z^2 - 5*z^3 9*x^3 + 15*x^2*y + 6*x^2*z - 5*x*y^2 + 23*x*y*z - 2*x*z^2 - 21*y^3 - 12*y^2*z + 3*y*z^2 + 3*z^3 12*x^3 - 5*x^2*y + 11*x^2*z - 43*x*y^2 + 15*x*y*z + 7*x*z^2 + 7*y^3 + y^2*z + 5*y*z^2 - z^3 9*x^3 + 9*x^2*y - 21*x^2*z - 3*x*y^2 - 45*x*y*z - 2*x*z^2 + 6*y^3 + 12*y^2*z + 22*y*z^2 + 9*z^3 3933 A 4: 9*x^3 - 3*x^2*z + 10*x*y^2 - 7*x*y*z + 22*x*z^2 + 5*y^3 + 2*y^2*z + 19*y*z^2 - 5*z^3 24*x^3 + 42*x^2*y + 3*x^2*z + 17*x*y^2 + 17*x*y*z + 5*x*z^2 + 25*y^3 + 3*y*z^2 - z^3 x^3 - 2*x^2*y - 3*x^2*z + 4*x*y^2 - 19*x*y*z - 3*x*z^2 + 3*y^3 - 53*y^2*z + 19*y*z^2 - 26*z^3 6*x^3 - 47*x^2*y - 4*x^2*z - 13*x*y^2 - 25*x*y*z + 2*x*z^2 - 23*y^3 - 3*y^2*z - z^3 3933 A 5: 59*x^3 - 33*x^2*y - 20*x^2*z - 6*x*y^2 - 7*x*y*z - 40*x*z^2 + 5*y^3 + 4*y^2*z - 13*y*z^2 - 6*z^3 9*x^3 - 12*x^2*y + 6*x^2*z - 2*x*y^2 - 31*x*y*z - 59*x*z^2 + 3*y^3 - 21*y^2*z - 6*y*z^2 + 27*z^3 9*x^3 + 12*x^2*y + 6*x^2*z - 36*x*y^2 + 51*x*y*z - 18*x*z^2 + 11*y^3 - 8*y^2*z - 33*y*z^2 + 9*z^3 3*x^3 + 23*x^2*y - 24*x^2*z + 19*x*y^2 - 5*x*y*z - 30*x*z^2 - 7*y^3 - 14*y^2*z + 11*y*z^2 + 15*z^3 3933 A 6: 3*x^3 - 7*x^2*y - 13*x^2*z - 4*x*y^2 + 19*x*y*z + 77*x*z^2 - 7*y^3 - 12*y^2*z + 9*y*z^2 - 103*z^3 7*x^3 - 2*x^2*y + x^2*z + 15*x*y^2 - 29*x*y*z - 2*x*z^2 - 21*y^3 - 36*y^2*z - 32*y*z^2 + 3*z^3 9*x^3 + 9*x^2*y - 24*x^2*z - 3*x*y^2 + 27*x*y*z + 36*x*z^2 + 6*y^3 - 28*y^2*z - 12*y*z^2 - 9*z^3 3*x^3 + 12*x^2*y + 12*x^2*z + 20*x*y^2 - 13*x*y*z + 5*x*z^2 - 3*y^3 - 9*y*z^2 + 39*z^3 3948 E 2: E[3] splits 3954 C 1: 56*x^3 + 34*x^2*y + 89*x^2*z - 62*x*y^2 - 31*x*y*z - x*z^2 - 10*y^3 - y^2*z - y*z^2 + 5*z^3 40*x^3 - x^2*y + 32*x^2*z + x*y^2 - 35*x*y*z - 32*x*z^2 + 5*y^3 + 29*y*z^2 - 60*z^3 45*x^3 + 48*x^2*y + 19*x*y^2 + 35*x*y*z - 16*x*z^2 - 44*y^3 + 31*y^2*z - 15*y*z^2 - 5*z^3 30*x^3 - 29*x^2*y - 3*x^2*z - 29*x*y^2 - 35*x*y*z - 25*y^3 + 16*y^2*z - 16*y*z^2 + 15*z^3 4046 J 2: E[3] splits 4050 JJ 2: E[3] splits 4158 AA 3: E[3] splits 4182 H 2: E[3] splits 4229 A 1: 4*x^3 + 8*x^2*y - 7*x^2*z + x*y^2 + x*y*z + 4*x*z^2 + y^3 + 4*y^2*z + 2*y*z^2 - 5*z^3 2*x^3 + x^2*y - 5*x^2*z + 11*x*y^2 - 5*x*y*z + 2*x*z^2 + 2*y^3 + 4*y^2*z - y*z^2 + 2*z^3 4*x^3 - x^2*y - 8*x^2*z + 2*x*y^2 - 3*x*y*z - 6*x*z^2 - y^3 - 6*y^2*z - z^3 2*x^3 - 2*x^2*y + x^2*z - x*y^2 + 9*x*y*z + 2*x*z^2 - 10*y^3 - 9*y^2*z - y*z^2 + 2*z^3 4290 N 2: E[3] splits 4290 O 3: E[3] splits 4290 O 4: E[3] splits 4343 B 1: 7*x^3 - 3*x^2*y + 7*x^2*z + 12*x*y^2 + 30*x*y*z - 4*x*z^2 + 17*y^3 - 15*y^2*z + 2*y*z^2 - 13*z^3 17*x^3 - 26*x^2*y + 32*x^2*z + 13*x*y^2 + 4*x*y*z - 4*x*z^2 - 15*y^3 + 15*y^2*z + 8*y*z^2 + z^3 12*x^3 - 5*x^2*y + 2*x^2*z + 3*x*y^2 - 40*x*y*z + 26*x*z^2 + 5*y^3 - 5*y^2*z - 4*y*z^2 + 31*z^3, 3*x^3 - 11*x^2*y + 26*x^2*z + 2*x*y^2 + 2*x*y*z + 10*x*z^2 - 11*y^3 + 10*y^2*z + 27*y*z^2 + 11*z^3 4356 H 2: E[3] splits 4356 J 2: E[3] splits 4524 E 3: E[3] splits 4524 E 4: (#Sha_an = 36!) E[3] splits 4524 F 2: E[3] splits 4563 G 4: E[3] splits 4590 Q 2: E[3] splits 4590 T 2: E[3] splits 4592 F 1: 8*x^3 + 8*x^2*y - 4*x^2*z - 14*x*y^2 + 26*x*y*z + 13*x*z^2 + 2*y^3 - 4*y^2*z + 43*y*z^2 - 13*z^3 42*x^3 + 14*x^2*y - 175*x^2*z + 10*x*y^2 - 16*x*y*z + 220*x*z^2 - 2*y^3 - 31*y^2*z - 38*y*z^2 - 107*z^3 2*x^3 + 18*x^2*y + 35*x^2*z - 24*x*y^2 - 6*x*y*z - 32*x*z^2 - 4*y^3 - 6*y^2*z - 8*y*z^2 - z^3 5*x^3 - x^2*y - x^2*z + 48*x*y^2 - 11*x*z^2 - 16*y^3 - 56*y^2*z - y*z^2 - z^3 4592 F 2: 22*x^3 + 20*x^2*y + 43*x^2*z - 92*x*y^2 + 46*x*y*z - 46*x*z^2 + 40*y^3 - 178*y^2*z - 132*y*z^2 - 2*z^3 44*x^3 - 56*x^2*y - 188*x^2*z - 43*x*y^2 + 88*x*y*z + 141*x*z^2 - y^3 - 19*y^2*z + 71*y*z^2 + 133*z^3 23*x^3 + 89*x^2*y + 23*x^2*z + 23*x*y^2 - 80*x*z^2 + y^3 + 23*y^2*z - 264*y*z^2 - 88*z^3 44*x^3 - 40*x^2*y + 86*x^2*z - 26*x*y^2 - 46*x*y*z - 132*x*z^2 + 2*y^3 - 89*y^2*z + 178*y*z^2 - 2*z^3 4606 B 1: 4*x^3 + 14*x^2*y + 14*x^2*z + 51*x*y^2 + 167*x*y*z + 183*x*z^2 - 41*y^3 - 188*y^2*z - 352*y*z^2 - 225*z^3 12*x^3 + 26*x^2*y - 27*x^2*z + 94*x*y^2 - 15*x*y*z + 39*x*z^2 + 22*y^3 + 35*y^2*z + y*z^2 + 5*z^3 25*x^3 - x^2*y + 54*x^2*z + 77*x*y^2 + 15*x*y*z + 41*x*z^2 + 26*y^3 + 10*y^2*z + 14*y*z^2 - 8*z^3 64*x^3 - 41*x^2*y + 26*x^2*z - x*y^2 + 19*x*y*z + 38*x*z^2 + 13*y^3 - 14*y^2*z + 27*y*z^2 - 30*z^3 4675 J 1: 13*x^3 - 3*x^2*y + 24*x^2*z + 6*x*y^2 - 6*x*y*z - 11*x*z^2 + y^3 + 16*y^2*z + 12*y*z^2 + 3*z^3 11*x^3 - 8*x^2*y - 19*x^2*z - 5*x*y^2 - 6*x*y*z + 24*x*z^2 + 5*y^3 + 5*y^2*z + 17*y*z^2 - z^3 x^3 + 3*x^2*y - 3*x^2*z + x*y^2 + 18*x*y*z + 6*x*z^2 - 12*y^3 + 21*y^2*z - 31*y*z^2 + 47*z^3 3*x^3 + 8*x^2*y + 5*x^2*z - 13*x*y^2 - 14*x*y*z + 4*x*z^2 + 17*y^3 - 19*y^2*z + 5*y*z^2 + 7*z^3 4800 S 2: E[3] splits 4800 W 3: E[3] splits 4800 W 6: E[3] splits 4800 W 7: E[3] splits 4800 W 8: E[3] splits 4830 CC 3: E[3] splits 4830 CC 6: E[3] splits 4830 CC 7: E[3] splits 4830 CC 8: E[3] splits 4830 EE 3: E[3] splits 4830 EE 4: E[3] splits 4914 N 1: E[3] splits 4914 N 3: E[3] splits 4950 D 3: E[3] splits 4950 D 4: E[3] splits 4963 C 1: x^3 - x^2*y + x^2*z - 2*x*y^2 + 5*x*y*z - 8*y^3 - y^2*z + y*z^2 + z^3 x^3 - x^2*y - x^2*z - 4*x*y^2 + 3*x*y*z + 2*x*z^2 + 6*y^3 + y^2*z + 3*y*z^2 - z^3 x^3 - 4*x^2*y - 3*x^2*z + x*y^2 + x*y*z + 2*x*z^2 - 3*y^3 + 3*y^2*z + y*z^2 - 2*z^3 x^3 - 3*x^2*z + 4*x*y^2 + x*y*z + x*z^2 + y^3 + 3*y^2*z + 2*y*z^2 + 3*z^3 4963 C 2: x^3 + 4*x^2*z + x*y^2 + 9*x*y*z - 10*x*z^2 - y^3 + 7*y^2*z + 17*y*z^2 + 26*z^3 13*x^3 + 14*x^2*y - 14*x^2*z + 10*x*y^2 + x*y*z + 4*x*z^2 - y^3 + 2*y^2*z - y*z^2 + z^3 3*x^3 + 12*x^2*y + 10*x^2*z + 7*x*y^2 + 5*x*y*z + 2*x*z^2 + 5*y^3 - y^2*z - 3*y*z^2 + 2*z^3 5*x^3 + x^2*y + 2*x^2*z + x*y^2 + 11*x*y*z - 7*x*z^2 + 2*y^3 - 3*y^2*z + 2*y*z^2 - 7*z^3