Cremona's table of elliptic curves

8712 = 2³ · 3² · 11²

Class	r	Atkin-Lehner	Eigenvalues
8712a (2 curves)	1	2+ 3+ 11+	2+ 3+  2 -2 11+ -2  2 -4
Curve Equation t Generators 8712a1 [0,0,0,-11979,322102] 2 [26:168:1] 8712a2 [0,0,0,-171699,27378670] 2 [83454:27560:343]
8712b (2 curves)	1	2+ 3+ 11+	2+ 3+ -2  2 11+  2  2  4
Curve Equation t Generators 8712b1 [0,0,0,-891,6534] 2 [-6:108:1] 8712b2 [0,0,0,-12771,555390] 2 [82:244:1]
8712c (2 curves)	0	2+ 3+ 11-	2+ 3+  0  2 11-  6  6  2
Curve Equation t 8712c1 [0,0,0,-1815,-23958] 2 8712c2 [0,0,0,-9075,311454] 2
8712d (1 curve)	0	2+ 3- 11+	2+ 3- -1  4 11+  4 -4 -4
Curve Equation t 8712d1 [0,0,0,15972,-644204] 1
8712e (2 curves)	0	2+ 3- 11+	2+ 3-  2 -2 11+  4  2  2
Curve Equation t 8712e1 [0,0,0,-759,7018] 2 8712e2 [0,0,0,1221,37510] 2
8712f (2 curves)	0	2+ 3- 11+	2+ 3- -2 -2 11+  0 -6  6
Curve Equation t 8712f1 [0,0,0,-7986,-805255] 2 8712f2 [0,0,0,-187671,-31243894] 2
8712g (2 curves)	0	2+ 3- 11+	2+ 3-  4  4 11+ -6  6  6
Curve Equation t 8712g1 [0,0,0,-8283,289190] 2 8712g2 [0,0,0,-12243,-15730] 2
8712h (1 curve)	1	2+ 3- 11-	2+ 3-  0 -1 11-  6 -4 -1
Curve Equation t Generators 8712h1 [0,0,0,-79860,9897316] 1 [242:-2178:1]
8712i (1 curve)	1	2+ 3- 11-	2+ 3-  1  0 11-  1  3  0
Curve Equation t Generators 8712i1 [0,0,0,2013,12782] 1 [31:324:1]
8712j (4 curves)	1	2+ 3- 11-	2+ 3-  2 -4 11- -6  6  8
Curve Equation t Generators 8712j1 [0,0,0,726,206305] 2 [-28:405:1] 8712j2 [0,0,0,-48279,3979690] 4 [335:5040:1] 8712j3 [0,0,0,-113619,-9101378] 2 [-154:2178:1] 8712j4 [0,0,0,-767019,258557398] 2 [231:9680:1]
8712k (4 curves)	1	2+ 3- 11-	2+ 3- -2  0 11- -2  6  0
Curve Equation t Generators 8712k1 [0,0,0,-13431,-577654] 2 [-65:144:1] 8712k2 [0,0,0,-35211,1770230] 4 [298:4212:1] 8712k3 [0,0,0,-514371,141972446] 2 [1606:58806:1] 8712k4 [0,0,0,95469,11832590] 2 [5142:164060:27]
8712l (1 curve)	1	2+ 3- 11-	2+ 3-  3  2 11-  0 -6 -4
Curve Equation t Generators 8712l1 [0,0,0,-4356,143748] 1 [22:242:1]
8712m (1 curve)	1	2+ 3- 11-	2+ 3- -3 -4 11- -3  3 -4
Curve Equation t Generators 8712m1 [0,0,0,-99,-594] 1 [15:36:1]
8712n (2 curves)	1	2+ 3- 11-	2+ 3- -4  2 11-  0 -6 -4
Curve Equation t Generators 8712n1 [0,0,0,-8729787,-9927809210] 2 [-1416601714:-47285469:830584] 8712n2 [0,0,0,-8686227,-10031786930] 2 [4034954390082:-468817244247451:284890312]
8712o (2 curves)	0	2- 3+ 11+	2- 3+  2  2 11+  2 -2  4
Curve Equation t 8712o1 [0,0,0,-99,-242] 2 8712o2 [0,0,0,-1419,-20570] 2
8712p (2 curves)	0	2- 3+ 11+	2- 3+ -2 -2 11+ -2 -2 -4
Curve Equation t 8712p1 [0,0,0,-107811,-8696754] 2 8712p2 [0,0,0,-1545291,-739224090] 2
8712q (2 curves)	1	2- 3+ 11-	2- 3+  0  2 11-  6 -6  2
Curve Equation t Generators 8712q1 [0,0,0,-16335,646866] 2 [-143:242:1] 8712q2 [0,0,0,-81675,-8409258] 2 [-197:188:1]
8712r (1 curve)	1	2- 3- 11+	2- 3- -1 -4 11+ -4  4  4
Curve Equation t Generators 8712r1 [0,0,0,132,484] 1 [0:22:1]
8712s (2 curves)	1	2- 3- 11+	2- 3-  2  2 11+ -4 -2 -2
Curve Equation t Generators 8712s1 [0,0,0,-91839,-9340958] 2 [-219:518:1] 8712s2 [0,0,0,147741,-49925810] 2 [92589:1064120:343]
8712t (2 curves)	1	2- 3- 11+	2- 3- -2  2 11+  0  6 -6
Curve Equation t Generators 8712t1 [0,0,0,-66,605] 2 [-2:27:1] 8712t2 [0,0,0,-1551,23474] 2 [-11:198:1]
8712u (2 curves)	1	2- 3- 11+	2- 3-  4 -4 11+  6 -6 -6
Curve Equation t Generators 8712u1 [0,0,0,-1002243,-384911890] 2 [-1328210:451170:2197] 8712u2 [0,0,0,-1481403,20936630] 2 [59136891710:-27441684625302:274625]
8712v (1 curve)	0	2- 3- 11-	2- 3-  0  1 11- -6  4  1
Curve Equation t 8712v1 [0,0,0,-660,-7436] 1
8712w (2 curves)	0	2- 3- 11-	2- 3-  0 -2 11-  0 -2 -8
Curve Equation t 8712w1 [0,0,0,-9075,98494] 2 8712w2 [0,0,0,34485,769318] 2
8712x (1 curve)	0	2- 3- 11-	2- 3-  1  0 11- -1 -3  0
Curve Equation t 8712x1 [0,0,0,243573,-17012842] 1
8712y (6 curves)	0	2- 3- 11-	2- 3-  2  0 11-  2  2  4
Curve Equation t 8712y1 [0,0,0,726,9317] 2 8712y2 [0,0,0,-4719,93170] 4 8712y3 [0,0,0,-26499,-1583890] 4 8712y4 [0,0,0,-70059,7136822] 2 8712y5 [0,0,0,-418539,-104219962] 2 8712y6 [0,0,0,17061,-6279658] 2
8712z (1 curve)	0	2- 3- 11-	2- 3- -3  4 11-  3 -3  4
Curve Equation t 8712z1 [0,0,0,-11979,790614] 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