Cremona's table of elliptic curves

12696 = 2³ · 3 · 23²

Class	r	Atkin-Lehner	Eigenvalues
12696a (2 curves)	0	2+ 3+ 23-	2+ 3+  0  2  0  2 -8 -6
Curve Equation t 12696a1 [0,-1,0,-1538508,-740537676] 2 12696a2 [0,-1,0,-24676968,-47174799204] 2
12696b (1 curve)	0	2+ 3+ 23-	2+ 3+  2  1  5  4 -2  0
Curve Equation t 12696b1 [0,-1,0,-196872,-33556500] 1
12696c (1 curve)	0	2+ 3+ 23-	2+ 3+  2  1 -6 -7 -2  0
Curve Equation t 12696c1 [0,-1,0,-4850577,4114201653] 1
12696d (2 curves)	0	2+ 3+ 23-	2+ 3+  2 -2  2 -2  4  0
Curve Equation t 12696d1 [0,-1,0,-34032,3435228] 2 12696d2 [0,-1,0,-605352,181458540] 2
12696e (1 curve)	0	2+ 3+ 23-	2+ 3+ -2 -1 -5  4  2  0
Curve Equation t 12696e1 [0,-1,0,-104145464,409115098764] 1
12696f (1 curve)	0	2+ 3+ 23-	2+ 3+ -2 -1  6 -7  2  0
Curve Equation t 12696f1 [0,-1,0,-9169,-334955] 1
12696g (1 curve)	0	2+ 3+ 23-	2+ 3+  3  4  0 -1  2  0
Curve Equation t 12696g1 [0,-1,0,4056,-3877668] 1
12696h (1 curve)	2	2+ 3+ 23-	2+ 3+ -3 -4  0 -1 -2  0
Curve Equation t Generators 12696h1 [0,-1,0,8,316] 1 [-6:4:1]&[1:18:1]
12696i (2 curves)	0	2+ 3+ 23-	2+ 3+ -4 -2  0  2  4  6
Curve Equation t 12696i1 [0,-1,0,1940,130036] 2 12696i2 [0,-1,0,-29800,1843996] 2
12696j (6 curves)	1	2- 3+ 23-	2- 3+  2  0 -4 -2 -2  4
Curve Equation t Generators 12696j1 [0,-1,0,353,-3272] 2 [1245:4207:125] 12696j2 [0,-1,0,-2292,-30780] 4 [60:210:1] 12696j3 [0,-1,0,-34032,-2404932] 2 [1118:36820:1] 12696j4 [0,-1,0,-12872,540540] 4 [139230:4621344:125] 12696j5 [0,-1,0,-203312,35352972] 2 [1674:11109:8] 12696j6 [0,-1,0,8288,2123308] 2 [-54096497:-809253180:753571]
12696k (1 curve)	1	2- 3+ 23-	2- 3+  2 -1  2  1 -2  0
Curve Equation t Generators 12696k1 [0,-1,0,16223,782293] 1 [57:24398:27]
12696l (2 curves)	1	2- 3+ 23-	2- 3+  2  2  0  2 -6  2
Curve Equation t Generators 12696l1 [0,-1,0,-105447,-13075920] 2 [69871601605:-912405256495:151419437] 12696l2 [0,-1,0,-44612,-28114332] 2 [1365572:29793798:2197]
12696m (1 curve)	1	2- 3+ 23-	2- 3+ -2  1 -2  1  2  0
Curve Equation t Generators 12696m1 [0,-1,0,31,-75] 1 [3:6:1]
12696n (2 curves)	1	2- 3+ 23-	2- 3+ -2 -2  0  2  6 -2
Curve Equation t Generators 12696n1 [0,-1,0,-199,1144] 2 [-15:23:1] 12696n2 [0,-1,0,-84,2340] 2 [8:46:1]
12696o (4 curves)	1	2- 3+ 23-	2- 3+ -2  4  4 -2  2  0
Curve Equation t Generators 12696o1 [0,-1,0,-109679,14017344] 4 [993443:24808315:1331] 12696o2 [0,-1,0,-112324,13308484] 4 [2884:153846:1] 12696o3 [0,-1,0,-397984,-81644900] 2 [996618:52338572:343] 12696o4 [0,-1,0,131016,62852508] 2 [145182894:7843351824:50653]
12696p (2 curves)	0	2- 3- 23-	2- 3-  2  2  4 -6  6  6
Curve Equation t 12696p1 [0,1,0,-3938052,-3019719168] 2 12696p2 [0,1,0,-63069672,-192808566720] 2
12696q (4 curves)	0	2- 3- 23-	2- 3-  2  4  0 -2  2  4
Curve Equation t 12696q1 [0,1,0,-2292,-407232] 4 12696q2 [0,1,0,-97512,-11681280] 4 12696q3 [0,1,0,-1557552,-748709472] 2 12696q4 [0,1,0,-160992,5331360] 2
12696r (2 curves)	0	2- 3- 23-	2- 3-  2 -4 -2  6  0  6
Curve Equation t 12696r1 [0,1,0,8,512] 2 12696r2 [0,1,0,-912,10080] 2
12696s (2 curves)	2	2- 3- 23-	2- 3- -2 -2 -4 -6 -6 -6
Curve Equation t Generators 12696s1 [0,1,0,-7444,245600] 2 [-46:702:1]&[8:432:1] 12696s2 [0,1,0,-119224,15805376] 2 [-376:2760:1]&[176:552:1]
12696t (2 curves)	0	2- 3- 23-	2- 3- -2  4  2  6  0 -6
Curve Equation t 12696t1 [0,1,0,4056,-6196608] 2 12696t2 [0,1,0,-482624,-126503904] 2

Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
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