Cremona's table of elliptic curves

12705 = 3 · 5 · 7 · 11²

Class	r	Atkin-Lehner	Eigenvalues
12705a (1 curve)	0	3+ 5+ 7+ 11-	0 3+ 5+ 7+ 11-  0 -3  3
Curve Equation t 12705a1 [0,-1,1,-15891,-2487013] 1
12705b (4 curves)	2	3+ 5+ 7+ 11-	-1 3+ 5+ 7+ 11-  2 -6 -4
Curve Equation t Generators 12705b1 [1,1,1,-24626,-1496626] 2 [-92:74:1]&[182:211:1] 12705b2 [1,1,1,-30071,-793132] 4 [-148:739:1]&[-111:1147:1] 12705b3 [1,1,1,-256946,49482368] 2 [-302:10133:1]&[-16:7328:1] 12705b4 [1,1,1,109684,-5936116] 2 [83:1894:1]&[2503:125072:1]
12705c (4 curves)	1	3+ 5+ 7- 11-	1 3+ 5+ 7- 11-  2 -6 -4
Curve Equation t Generators 12705c1 [1,1,0,-1333,14392] 2 [424:8500:1] 12705c2 [1,1,0,-6778,-204497] 4 [154:1483:1] 12705c3 [1,1,0,-106603,-13441292] 2 [3894:54785:8] 12705c4 [1,1,0,5927,-867698] 2 [72072:817739:512]
12705d (1 curve)	1	3+ 5+ 7- 11-	-2 3+ 5+ 7- 11-  2  3  5
Curve Equation t Generators 12705d1 [0,-1,1,1003534,-382978168] 1 [598:20751:1]
12705e (4 curves)	1	3+ 5- 7+ 11-	-1 3+ 5- 7+ 11-  2  6 -4
Curve Equation t Generators 12705e1 [1,1,1,-1965345,1059670470] 4 [810:-355:1] 12705e2 [1,1,1,-1965950,1058984642] 4 [-60:34333:1] 12705e3 [1,1,1,-2505005,431309000] 2 [-132:27628:1] 12705e4 [1,1,1,-1436575,1642779392] 2 [65:39333:1]
12705f (1 curve)	1	3+ 5- 7+ 11-	2 3+ 5- 7+ 11-  2  3 -1
Curve Equation t Generators 12705f1 [0,-1,1,-40,-10869] 1 [186:117:8]
12705g (6 curves)	0	3+ 5- 7- 11-	1 3+ 5- 7- 11-  2  6  4
Curve Equation t 12705g1 [1,1,0,-32067,-2223624] 2 12705g2 [1,1,0,-32672,-2136141] 4 12705g3 [1,1,0,-105877,10704016] 4 12705g4 [1,1,0,30853,-9365286] 2 12705g5 [1,1,0,-1603252,780654241] 4 12705g6 [1,1,0,220218,63987939] 2
12705h (2 curves)	0	3- 5+ 7+ 11+	1 3- 5+ 7+ 11+ -4 -4 -4
Curve Equation t 12705h1 [1,0,1,-2653654,1588689947] 2 12705h2 [1,0,1,-7505149,-5876790559] 2
12705i (2 curves)	1	3- 5+ 7+ 11-	0 3- 5+ 7+ 11-  4 -3  1
Curve Equation t Generators 12705i1 [0,1,1,-161,45656] 1 [-26:181:1] 12705i2 [0,1,1,-101801,12468605] 1 [51:2722:1]
12705j (2 curves)	1	3- 5+ 7- 11+	-1 3- 5+ 7- 11+  4  4  4
Curve Equation t Generators 12705j1 [1,0,0,-21931,-1195600] 2 [-91:266:1] 12705j2 [1,0,0,-62026,4409681] 2 [-229:2687:1]
12705k (4 curves)	0	3- 5+ 7- 11-	-1 3- 5+ 7- 11-  2  2  4
Curve Equation t 12705k1 [1,0,0,-426,24531] 2 12705k2 [1,0,0,-15551,741456] 4 12705k3 [1,0,0,-24626,-225939] 2 12705k4 [1,0,0,-248476,47652551] 2
12705l (1 curve)	0	3- 5+ 7- 11-	2 3- 5+ 7- 11-  2 -1  7
Curve Equation t 12705l1 [0,1,1,-15286,-734915] 1
12705m (6 curves)	0	3- 5- 7+ 11-	1 3- 5- 7+ 11-  2 -2 -4
Curve Equation t 12705m1 [1,0,1,4232,30787601] 2 12705m2 [1,0,1,-1448373,658894003] 4 12705m3 [1,0,1,-3078848,-1096801477] 2 12705m4 [1,0,1,-23059578,42619209631] 4 12705m5 [1,0,1,-368953203,2727722241781] 2 12705m6 [1,0,1,-22945233,43062822493] 2
12705n (4 curves)	0	3- 5- 7+ 11-	-1 3- 5- 7+ 11-  6 -2  8
Curve Equation t 12705n1 [1,0,0,-305,-1968] 2 12705n2 [1,0,0,-910,8075] 4 12705n3 [1,0,0,-13615,610292] 2 12705n4 [1,0,0,2115,51030] 2
12705o (4 curves)	0	3- 5- 7+ 11-	-1 3- 5- 7+ 11- -6 -2 -4
Curve Equation t 12705o1 [1,0,0,-382060,-6242785] 4 12705o2 [1,0,0,-4351465,-3485823208] 4 12705o3 [1,0,0,-69577120,-223387596475] 2 12705o4 [1,0,0,-2636290,-6261319393] 2
12705p (2 curves)	0	3- 5- 7+ 11-	2 3- 5- 7+ 11-  6  7  5
Curve Equation t 12705p1 [0,1,1,-1081780,-507519941] 1 12705p2 [0,1,1,-3241630,42469124539] 1
12705q (1 curve)	1	3- 5- 7- 11-	0 3- 5- 7- 11-  4  5 -1
Curve Equation t Generators 12705q1 [0,1,1,65905,-3375619] 1 [535:13612:1]

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

Part of Computational Number Theory
Back to Tables and computations