Cremona's table of elliptic curves

31200 = 2⁵ · 3 · 5² · 13

Class	r	Atkin-Lehner	Eigenvalues
31200a (2 curves)	1	2+ 3+ 5+ 13+	2+ 3+ 5+ -2  0 13+ -2 -2
Curve Equation t Generators 31200a1 [0,-1,0,-458,-3588] 2 [-12:6:1] 31200a2 [0,-1,0,-833,3537] 2 [-23:100:1]
31200b (1 curve)	1	2+ 3+ 5+ 13+	2+ 3+ 5+  3  3 13+  3 -2
Curve Equation t Generators 31200b1 [0,-1,0,116867,3231637] 1 [-411:32500:27]
31200c (4 curves)	1	2+ 3+ 5+ 13+	2+ 3+ 5+  4  0 13+ -2 -8
Curve Equation t Generators 31200c1 [0,-1,0,-406758,56638512] 4 [141947:12157894:2197] 31200c2 [0,-1,0,1304367,407419137] 2 [17112:2243475:1] 31200c3 [0,-1,0,-2938008,-1897486488] 2 [337206145824198466:-20444688611103777475:76020262981928] 31200c4 [0,-1,0,-5688008,5221701012] 2 [1228:9334:1]
31200d (4 curves)	0	2+ 3+ 5+ 13-	2+ 3+ 5+  0  0 13- -2  4
Curve Equation t 31200d1 [0,-1,0,-1658,-23688] 4 31200d2 [0,-1,0,1592,-108188] 2 31200d3 [0,-1,0,-5408,126312] 2 31200d4 [0,-1,0,-26033,-1608063] 2
31200e (1 curve)	0	2+ 3+ 5+ 13-	2+ 3+ 5+  1 -3 13-  3  6
Curve Equation t 31200e1 [0,-1,0,4467,418437] 1
31200f (1 curve)	0	2+ 3+ 5+ 13-	2+ 3+ 5+ -1 -3 13- -3  6
Curve Equation t 31200f1 [0,-1,0,-2349133,-1402142363] 1
31200g (2 curves)	0	2+ 3+ 5+ 13-	2+ 3+ 5+ -2  0 13-  0 -6
Curve Equation t 31200g1 [0,-1,0,-49158,-5036688] 2 31200g2 [0,-1,0,-830408,-290974188] 2
31200h (2 curves)	2	2+ 3+ 5+ 13-	2+ 3+ 5+ -2 -6 13-  2 -6
Curve Equation t Generators 31200h1 [0,-1,0,-358,2212] 2 [-18:50:1]&[-9:68:1] 31200h2 [0,-1,0,767,12337] 2 [13:-156:1]&[-8:75:1]
31200i (1 curve)	0	2+ 3+ 5+ 13-	2+ 3+ 5+  3 -3 13-  7 -8
Curve Equation t 31200i1 [0,-1,0,-490833,132789537] 1
31200j (1 curve)	0	2+ 3+ 5+ 13-	2+ 3+ 5+  4  0 13-  0  3
Curve Equation t 31200j1 [0,-1,0,312,-17208] 1
31200k (1 curve)	0	2+ 3+ 5- 13+	2+ 3+ 5-  3  3 13+ -7  8
Curve Equation t 31200k1 [0,-1,0,-19633,-1054463] 1
31200l (2 curves)	0	2+ 3+ 5- 13+	2+ 3+ 5-  4 -2 13+  0  2
Curve Equation t 31200l1 [0,-1,0,-198,-1008] 2 31200l2 [0,-1,0,-248,-408] 2
31200m (1 curve)	1	2+ 3+ 5- 13-	2+ 3+ 5-  3  5 13- -5  4
Curve Equation t Generators 31200m1 [0,-1,0,-33,-32463] 1 [177:-2340:1]
31200n (4 curves)	0	2+ 3- 5+ 13+	2+ 3- 5+  0  4 13+  6 -8
Curve Equation t 31200n1 [0,1,0,-5858,-173712] 4 31200n2 [0,1,0,-2608,-362212] 2 31200n3 [0,1,0,-9233,45663] 2 31200n4 [0,1,0,-93608,-11054712] 2
31200o (2 curves)	0	2+ 3- 5+ 13+	2+ 3- 5+  2  0 13+ -2  2
Curve Equation t 31200o1 [0,1,0,-458,3588] 2 31200o2 [0,1,0,-833,-3537] 2
31200p (4 curves)	0	2+ 3- 5+ 13+	2+ 3- 5+ -4  0 13+ -2  8
Curve Equation t 31200p1 [0,1,0,-406758,-56638512] 4 31200p2 [0,1,0,1304367,-407419137] 2 31200p3 [0,1,0,-2938008,1897486488] 2 31200p4 [0,1,0,-5688008,-5221701012] 2
31200q (1 curve)	1	2+ 3- 5+ 13-	2+ 3- 5+  1 -1 13-  5  2
Curve Equation t Generators 31200q1 [0,1,0,-3133,68363] 1 [-7:300:1]
31200r (1 curve)	1	2+ 3- 5+ 13-	2+ 3- 5+  1  3 13- -3 -6
Curve Equation t Generators 31200r1 [0,1,0,-2349133,1402142363] 1 [82371:4062500:27]
31200s (1 curve)	1	2+ 3- 5+ 13-	2+ 3- 5+ -1 -1 13-  3 -6
Curve Equation t Generators 31200s1 [0,1,0,-13533,-1096437] 1 [1373:50700:1]
31200t (1 curve)	1	2+ 3- 5+ 13-	2+ 3- 5+ -1  3 13-  3 -6
Curve Equation t Generators 31200t1 [0,1,0,4467,-418437] 1 [93:900:1]
31200u (1 curve)	1	2+ 3- 5+ 13-	2+ 3- 5+ -1  5 13-  3  0
Curve Equation t Generators 31200u1 [0,1,0,47,-97] 1 [2:3:1]
31200v (2 curves)	1	2+ 3- 5+ 13-	2+ 3- 5+  2  0 13-  0  6
Curve Equation t Generators 31200v1 [0,1,0,-49158,5036688] 2 [-102:3000:1] 31200v2 [0,1,0,-830408,290974188] 2 [2863:146250:1]
31200w (2 curves)	1	2+ 3- 5+ 13-	2+ 3- 5+  2  2 13- -6 -2
Curve Equation t Generators 31200w1 [0,1,0,-72558,7496388] 2 [144:234:1] 31200w2 [0,1,0,-62433,9673263] 2 [-177:3900:1]
31200x (2 curves)	1	2+ 3- 5+ 13-	2+ 3- 5+ -2  2 13-  2  2
Curve Equation t Generators 31200x1 [0,1,0,-264758,-52428012] 2 [-296:306:1] 31200x2 [0,1,0,-173633,-88969137] 2 [703:11700:1]
31200y (1 curve)	1	2+ 3- 5+ 13-	2+ 3- 5+ -4  0 13-  0 -3
Curve Equation t Generators 31200y1 [0,1,0,312,17208] 1 [-18:78:1]
31200z (1 curve)	1	2+ 3- 5- 13+	2+ 3- 5- -1 -5 13+ -3  0
Curve Equation t Generators 31200z1 [0,1,0,1167,14463] 1 [33:300:1]
31200ba (2 curves)	1	2+ 3- 5- 13+	2+ 3- 5- -4  2 13+  0 -2
Curve Equation t Generators 31200ba1 [0,1,0,-198,1008] 2 [9:6:1] 31200ba2 [0,1,0,-248,408] 2 [-2:30:1]
31200bb (1 curve)	2	2+ 3- 5- 13-	2+ 3- 5- -3 -5 13- -5 -4
Curve Equation t Generators 31200bb1 [0,1,0,-33,32463] 1 [-27:120:1]&[-21:156:1]
31200bc (4 curves)	0	2- 3+ 5+ 13+	2- 3+ 5+  0  4 13+  2 -4
Curve Equation t 31200bc1 [0,-1,0,-40041158,-97503029688] 4 31200bc2 [0,-1,0,-37307408,-111390479688] 2 31200bc3 [0,-1,0,-42787408,-83359842188] 2 31200bc4 [0,-1,0,-640646033,-6241090296063] 2
31200bd (4 curves)	0	2- 3+ 5+ 13+	2- 3+ 5+  0 -4 13+  6  8
Curve Equation t 31200bd1 [0,-1,0,-5858,173712] 4 31200bd2 [0,-1,0,-2608,362212] 2 31200bd3 [0,-1,0,-9233,-45663] 2 31200bd4 [0,-1,0,-93608,11054712] 2
31200be (4 curves)	2	2- 3+ 5+ 13+	2- 3+ 5+  0 -4 13+ -6 -4
Curve Equation t Generators 31200be1 [0,-1,0,-1158,12312] 4 [-37:56:1]&[-12:156:1] 31200be2 [0,-1,0,2592,72312] 2 [77:850:1]&[761:21028:1] 31200be3 [0,-1,0,-6033,-168063] 2 [-43:100:1]&[-37:56:1] 31200be4 [0,-1,0,-17408,889812] 2 [-148:450:1]&[52:350:1]
31200bf (2 curves)	0	2- 3+ 5+ 13+	2- 3+ 5+  2 -4 13+  0  6
Curve Equation t 31200bf1 [0,-1,0,-1758,-46488] 2 31200bf2 [0,-1,0,-33008,-2296488] 2
31200bg (2 curves)	0	2- 3+ 5+ 13+	2- 3+ 5+  2 -4 13+  6 -6
Curve Equation t 31200bg1 [0,-1,0,-2458,21412] 2 31200bg2 [0,-1,0,-32833,2299537] 2
31200bh (1 curve)	0	2- 3+ 5+ 13+	2- 3+ 5+  3 -5 13+  5 -4
Curve Equation t 31200bh1 [0,-1,0,-833,4059537] 1
31200bi (1 curve)	0	2- 3+ 5+ 13+	2- 3+ 5+  5 -1 13+ -3  6
Curve Equation t 31200bi1 [0,-1,0,467,26437] 1
31200bj (1 curve)	1	2- 3+ 5+ 13-	2- 3+ 5+  1  1 13-  3  6
Curve Equation t Generators 31200bj1 [0,-1,0,-13533,1096437] 1 [-73:1300:1]
31200bk (1 curve)	1	2- 3+ 5+ 13-	2- 3+ 5+  1 -5 13-  3  0
Curve Equation t Generators 31200bk1 [0,-1,0,47,97] 1 [1:12:1]
31200bl (1 curve)	1	2- 3+ 5+ 13-	2- 3+ 5+ -1  1 13-  5 -2
Curve Equation t Generators 31200bl1 [0,-1,0,-3133,-68363] 1 [107:900:1]
31200bm (1 curve)	1	2- 3+ 5+ 13-	2- 3+ 5+ -1 -3 13-  5 -2
Curve Equation t Generators 31200bm1 [0,-1,0,-1121133,457301637] 1 [427:7500:1]
31200bn (2 curves)	1	2- 3+ 5+ 13-	2- 3+ 5+  2  0 13- -4 -2
Curve Equation t Generators 31200bn1 [0,-1,0,242,-488] 2 [3:16:1] 31200bn2 [0,-1,0,-1008,-2988] 2 [-28:50:1]
31200bo (2 curves)	1	2- 3+ 5+ 13-	2- 3+ 5+  2 -2 13-  2 -2
Curve Equation t Generators 31200bo1 [0,-1,0,-264758,52428012] 2 [223:2104:1] 31200bo2 [0,-1,0,-173633,88969137] 2 [-253:10800:1]
31200bp (2 curves)	1	2- 3+ 5+ 13-	2- 3+ 5+ -2 -2 13- -6  2
Curve Equation t Generators 31200bp1 [0,-1,0,-72558,-7496388] 2 [-157:26:1] 31200bp2 [0,-1,0,-62433,-9673263] 2 [567:11700:1]
31200bq (4 curves)	1	2- 3+ 5+ 13-	2- 3+ 5+ -4  4 13- -2 -4
Curve Equation t Generators 31200bq1 [0,-1,0,-2158,-25688] 4 [-29:108:1] 31200bq2 [0,-1,0,5967,-180063] 2 [37:300:1] 31200bq3 [0,-1,0,-13408,581812] 4 [-92:1014:1] 31200bq4 [0,-1,0,-31408,-2131688] 2 [-2733:316:27]
31200br (1 curve)	1	2- 3+ 5- 13+	2- 3+ 5-  1  5 13+ -3  0
Curve Equation t Generators 31200br1 [0,-1,0,1167,-14463] 1 [17:100:1]
31200bs (1 curve)	1	2- 3+ 5- 13+	2- 3+ 5-  4  0 13+  0 -3
Curve Equation t Generators 31200bs1 [0,-1,0,7792,2135412] 1 [-108:150:1]
31200bt (2 curves)	0	2- 3+ 5- 13-	2- 3+ 5-  4  2 13-  0 -2
Curve Equation t 31200bt1 [0,-1,0,-4958,135912] 2 31200bt2 [0,-1,0,-6208,63412] 2
31200bu (4 curves)	1	2- 3- 5+ 13+	2- 3- 5+  0  4 13+ -6  4
Curve Equation t Generators 31200bu1 [0,1,0,-1158,-12312] 4 [6154:170625:8] 31200bu2 [0,1,0,2592,-72312] 2 [265503:1504250:9261] 31200bu3 [0,1,0,-6033,168063] 2 [143:1500:1] 31200bu4 [0,1,0,-17408,-889812] 2 [167118:4578875:216]
31200bv (4 curves)	1	2- 3- 5+ 13+	2- 3- 5+  0 -4 13+  2  4
Curve Equation t Generators 31200bv1 [0,1,0,-40041158,97503029688] 4 [-2447:425250:1] 31200bv2 [0,1,0,-37307408,111390479688] 2 [-2357:431550:1] 31200bv3 [0,1,0,-42787408,83359842188] 2 [139594:17250975:8] 31200bv4 [0,1,0,-640646033,6241090296063] 2 [14623:2100:1]
31200bw (2 curves)	1	2- 3- 5+ 13+	2- 3- 5+ -2  4 13+  0 -6
Curve Equation t Generators 31200bw1 [0,1,0,-1758,46488] 2 [29:144:1] 31200bw2 [0,1,0,-33008,2296488] 2 [78:450:1]
31200bx (2 curves)	1	2- 3- 5+ 13+	2- 3- 5+ -2  4 13+  6  6
Curve Equation t Generators 31200bx1 [0,1,0,-2458,-21412] 2 [-28:162:1] 31200bx2 [0,1,0,-32833,-2299537] 2 [-103:12:1]
31200by (1 curve)	1	2- 3- 5+ 13+	2- 3- 5+ -3 -3 13+  3  2
Curve Equation t Generators 31200by1 [0,1,0,116867,-3231637] 1 [293:-7500:1]
31200bz (1 curve)	1	2- 3- 5+ 13+	2- 3- 5+ -3  5 13+  5  4
Curve Equation t Generators 31200bz1 [0,1,0,-833,-4059537] 1 [277:4128:1]
31200ca (1 curve)	1	2- 3- 5+ 13+	2- 3- 5+ -5  1 13+ -3 -6
Curve Equation t Generators 31200ca1 [0,1,0,467,-26437] 1 [193:2700:1]
31200cb (4 curves)	0	2- 3- 5+ 13-	2- 3- 5+  0  0 13- -2 -4
Curve Equation t 31200cb1 [0,1,0,-1658,23688] 4 31200cb2 [0,1,0,1592,108188] 2 31200cb3 [0,1,0,-5408,-126312] 2 31200cb4 [0,1,0,-26033,1608063] 2
31200cc (1 curve)	0	2- 3- 5+ 13-	2- 3- 5+  1  3 13-  5  2
Curve Equation t 31200cc1 [0,1,0,-1121133,-457301637] 1
31200cd (2 curves)	0	2- 3- 5+ 13-	2- 3- 5+  2  6 13-  2  6
Curve Equation t 31200cd1 [0,1,0,-358,-2212] 2 31200cd2 [0,1,0,767,-12337] 2
31200ce (2 curves)	0	2- 3- 5+ 13-	2- 3- 5+ -2  0 13- -4  2
Curve Equation t 31200ce1 [0,1,0,242,488] 2 31200ce2 [0,1,0,-1008,2988] 2
31200cf (1 curve)	0	2- 3- 5+ 13-	2- 3- 5+ -3  3 13-  7  8
Curve Equation t 31200cf1 [0,1,0,-490833,-132789537] 1
31200cg (4 curves)	0	2- 3- 5+ 13-	2- 3- 5+  4 -4 13- -2  4
Curve Equation t 31200cg1 [0,1,0,-2158,25688] 4 31200cg2 [0,1,0,5967,180063] 4 31200cg3 [0,1,0,-13408,-581812] 2 31200cg4 [0,1,0,-31408,2131688] 2
31200ch (1 curve)	2	2- 3- 5- 13+	2- 3- 5- -3 -3 13+ -7 -8
Curve Equation t Generators 31200ch1 [0,1,0,-19633,1054463] 1 [59:324:1]&[83:60:1]
31200ci (1 curve)	0	2- 3- 5- 13+	2- 3- 5- -4  0 13+  0  3
Curve Equation t 31200ci1 [0,1,0,7792,-2135412] 1
31200cj (2 curves)	1	2- 3- 5- 13-	2- 3- 5- -4 -2 13-  0  2
Curve Equation t Generators 31200cj1 [0,1,0,-4958,-135912] 2 [3958:249000:1] 31200cj2 [0,1,0,-6208,-63412] 2 [-73:78:1]

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