unknown terminal "dumb"
[was@form mathcamp]$ Magma V2.8-BETA   Sun Jul 15 2001 22:52:24 on form     [Seed = 1]
Linked at:        Fri Jul 06 2001 16:37:08
Type ? for help.  Type <Ctrl>-D to quit.
load "code.m";

Loading startup file "/home/was/magma/local/emacs.m"

Loading "/home/was/magma/local/init.m"
> Loading "code.m"
> 
> 
> CongruentTriangle(6);
A solution is  (-3 : 9 : 1)
3 4 5
> TunnelsCriterion(1);
First set :=  [ <0, -1, 0>, <0, 1, 0> ]
Second set :=  [ <0, -1, 0>, <0, 1, 0> ]
false
> TunnelsCriterion(2);
First set :=  [ <0, -1, 0>, <0, 1, 0> ]
Second set :=  [ <0, -1, 0>, <0, 1, 0> ]
false
> TunnelsCriterion(6);
First set :=  []
Second set :=  []
true
> TunnelsCriterion(6);
First set :=  []
Second set :=  []
true
> load "code.m";
Loading "code.m"
> c := [n : n in [1..50] | TunnelsCriterion(n)];
> c;
[ 5, 6, 7, 13, 14, 15, 20, 21, 22, 23, 24, 28, 29, 30, 31, 34, 37, 38, 39, 41, 45, 46, 47 ]
> c := [n : n in [1..100] | TunnelsCriterion(n)];
> c;
[ 5, 6, 7, 13, 14, 15, 20, 21, 22, 23, 24, 28, 29, 30, 31, 34, 37, 38, 39, 41, 45, 46, 47, 52, 53, 54, 55, 56, 60, 61, 62, 63, 65, 69, 70, 71, 77, 78, 79, 80, 84, 85, 86, 87, 88, 92, 93, 94, 95, 96 ]
> c := [n : n in [1..100] | TunnelsCriterion(n) and IsSquareFree(n)];
> c;
[ 5, 6, 7, 13, 14, 15, 21, 22, 23, 29, 30, 31, 34, 37, 38, 39, 41, 46, 47, 53, 55, 61, 62, 65, 69, 70, 71, 77, 78, 79, 85, 86, 87, 93, 94, 95 ]
> CongruentTriangle(20);
A solution is  (-16 : 48 : 1)
3 40/3 41/3
> a,b,c := CongruentTriangle(20);
A solution is  (-16 : 48 : 1)
> a^2+b^2-c^2;
0
> a^2;
9
> a^2+b^2;
1681/9
> c^2;
1681/9
> 1/2*a*b;
20
> #c;

>> #c;
   ^
Runtime error in '#': Bad argument types
Argument types given: FldRatElt
> c := [ 5, 6, 7, 13, 14, 15, 21, 22, 23, 29, 30, 31, 34, 37, 38, 39, 41, 46, 47, 53, 55, 61, 62, 65, 69, 70, 71, 77, 78, 79, 85, 86, 87, 93, 94, 95 ];
> #c;
36
> CongruentTriangle(13);
A solution is  (-36/25 : 1938/125 : 1)
323/30 780/323 106921/9690
> CongruentTriangle(14);
A solution is  (18 : 48 : 1)
8/3 21/2 65/6
> CongruentTriangle(15);
A solution is  (-9 : 36 : 1)
4 15/2 17/2
> for i in [1..20] do print i, CongruentTriangle(c[i]); end for;
A solution is  (-4 : 6 : 1)
1 3/2 20/3 41/6
A solution is  (-3 : 9 : 1)
2 3 4 5
A solution is  (25 : 120 : 1)
3 24/5 35/12 337/60
A solution is  (-36/25 : 1938/125 : 1)
4 323/30 780/323 106921/9690
A solution is  (18 : 48 : 1)
5 8/3 21/2 65/6
A solution is  (-9 : 36 : 1)
6 4 15/2 17/2
A solution is  (-3 : 36 : 1)
7 12 7/2 25/2
A solution is  (2178 : 101640 : 1)
8 140/3 33/35 4901/105
A solution is  (559728/17689 : -287596140/2352637 : 1)
9 41496/3485 80155/20748 905141617/72306780
Warning: n (7) is not a power of 2
A solution is  (-4900/169 : 6930/2197 : 1)
10 99/910 52780/99 48029801/90090
A solution is  (-20 : 100 : 1)
11 5 12 13
A solution is  (1681/49 : 29520/343 : 1)
12 720/287 8897/360 2566561/103320
A solution is  (-16 : 120 : 1)
13 15/2 136/15 353/30
Warning: rank computed (0) is only a lower bound
(It may still be correct, though)
37 is probably a congruent number, but I can't find the representation.
14 0
Warning: n (7) is not a power of 2
A solution is  (-1922/81 : 105400/729 : 1)
15 1700/279 5301/425 1646021/118575
A solution is  (-36 : 90 : 1)
16 5/2 156/5 313/10
Height bound (15.1528) on point search is too large -- reducing to 15.0000
This means that the computed group may only generate a group of finite
index in the actual group.

[Interrupted]
> 
> 
> 
> c[14];
37
> CongruentNumberCurve(37);
Elliptic Curve defined by y^2 = x^3 - 1369*x over Rational Field
>