Cremona's table of elliptic curves

3136 = 2⁶ · 7²

Class	r	Atkin-Lehner	Eigenvalues
3136a (1 curve)	1	2+ 7+	2+  1  1 7+ -3  6 -5 -1
Curve Equation t Generators 3136a1 [0,1,0,-65,167] 1 [2:7:1]
3136b (2 curves)	1	2+ 7+	2+ -1 -3 7+  3 -2  3  1
Curve Equation t Generators 3136b1 [0,-1,0,-457,-559] 1 [-16:49:1] 3136b2 [0,-1,0,-27897,-1784159] 1 [-96:1:1]
3136c (1 curve)	1	2+ 7+	2+ -3  1 7+  1 -2  3 -5
Curve Equation t Generators 3136c1 [0,0,0,-1372,-19208] 1 [-19:1:1]
3136d (4 curves)	0	2+ 7-	2+  0  0 7- -4  0  0  0
Curve Equation t 3136d1 [0,0,0,-140,-784] 2 3136d2 [0,0,0,-2380,-44688] 2 3136d3 [0,0,0,-6860,268912] 2 3136d4 [0,0,0,-116620,15327984] 2
3136e (4 curves)	0	2+ 7-	2+  0  2 7-  4  2  6  8
Curve Equation t 3136e1 [0,0,0,196,-5488] 2 3136e2 [0,0,0,-3724,-82320] 4 3136e3 [0,0,0,-58604,-5460560] 2 3136e4 [0,0,0,-11564,378672] 2
3136f (2 curves)	0	2+ 7-	2+  1  3 7-  3  2 -3 -1
Curve Equation t 3136f1 [0,1,0,-9,-1] 1 3136f2 [0,1,0,-569,5039] 1
3136g (1 curve)	0	2+ 7-	2+ -1 -1 7- -3 -6  5  1
Curve Equation t 3136g1 [0,-1,0,-3201,-63671] 1
3136h (2 curves)	0	2+ 7-	2+  2  2 7- -4  6  4  6
Curve Equation t 3136h1 [0,-1,0,-457,-19767] 2 3136h2 [0,-1,0,-14177,-642655] 2
3136i (2 curves)	0	2+ 7-	2+  2 -2 7-  4 -6 -4  6
Curve Equation t 3136i1 [0,-1,0,-9,-55] 2 3136i2 [0,-1,0,-289,-1791] 2
3136j (2 curves)	0	2+ 7-	2+  2 -4 7-  0  0  2 -2
Curve Equation t 3136j1 [0,-1,0,-65,11201] 2 3136j2 [0,-1,0,-7905,269921] 2
3136k (6 curves)	0	2+ 7-	2+ -2  0 7-  0 -4 -6  2
Curve Equation t 3136k1 [0,1,0,-1633,-51969] 2 3136k2 [0,1,0,-32993,-2316161] 2 3136k3 [0,1,0,14047,1080127] 2 3136k4 [0,1,0,-111393,11692351] 2 3136k5 [0,1,0,-534753,150770815] 2 3136k6 [0,1,0,-8562913,9641661567] 2
3136l (2 curves)	0	2+ 7-	2+ -2  2 7-  4  6  4 -6
Curve Equation t 3136l1 [0,1,0,-457,19767] 2 3136l2 [0,1,0,-14177,642655] 2
3136m (2 curves)	2	2+ 7-	2+ -2 -2 7- -4 -6 -4 -6
Curve Equation t Generators 3136m1 [0,1,0,-9,55] 2 [-3:8:1]&[-1:8:1] 3136m2 [0,1,0,-289,1791] 2 [-19:28:1]&[-5:56:1]
3136n (1 curve)	0	2+ 7-	2+  3 -1 7-  1  2 -3  5
Curve Equation t 3136n1 [0,0,0,-28,56] 1
3136o (2 curves)	0	2- 7+	2-  1 -3 7+ -3 -2  3 -1
Curve Equation t 3136o1 [0,1,0,-457,559] 1 3136o2 [0,1,0,-27897,1784159] 1
3136p (1 curve)	0	2- 7+	2- -1  1 7+  3  6 -5  1
Curve Equation t 3136p1 [0,-1,0,-65,-167] 1
3136q (1 curve)	0	2- 7+	2-  3  1 7+ -1 -2  3  5
Curve Equation t 3136q1 [0,0,0,-1372,19208] 1
3136r (4 curves)	1	2- 7-	2-  0  0 7-  4  0  0  0
Curve Equation t Generators 3136r1 [0,0,0,-140,784] 2 [0:28:1] 3136r2 [0,0,0,-2380,44688] 2 [21:63:1] 3136r3 [0,0,0,-6860,-268912] 2 [5506:408512:1] 3136r4 [0,0,0,-116620,-15327984] 2 [12105600:896827212:2197]
3136s (4 curves)	1	2- 7-	2-  0  2 7- -4  2  6 -8
Curve Equation t Generators 3136s1 [0,0,0,196,5488] 2 [-6:64:1] 3136s2 [0,0,0,-3724,82320] 4 [92:720:1] 3136s3 [0,0,0,-11564,-378672] 2 [266:3920:1] 3136s4 [0,0,0,-58604,5460560] 2 [28:1960:1]
3136t (4 curves)	1	2- 7-	2-  0 -2 7-  0  6 -2  0
Curve Equation t Generators 3136t1 [0,0,0,49,0] 2 [48:260:27] 3136t2 [0,0,0,-196,0] 4 [18:48:1] 3136t3 [0,0,0,-2156,-38416] 2 [-26:8:1] 3136t4 [0,0,0,-2156,38416] 2 [0:196:1]
3136u (2 curves)	1	2- 7-	2-  0  4 7-  0 -4 -8  0
Curve Equation t Generators 3136u1 [0,0,0,-343,0] 2 [2420:3102:125] 3136u2 [0,0,0,1372,0] 2 [50:440:1]
3136v (2 curves)	1	2- 7-	2-  0 -4 7-  0  4  8  0
Curve Equation t Generators 3136v1 [0,0,0,-7,0] 2 [4:6:1] 3136v2 [0,0,0,28,0] 2 [2:8:1]
3136w (1 curve)	1	2- 7-	2-  1 -1 7-  3 -6  5 -1
Curve Equation t Generators 3136w1 [0,1,0,-3201,63671] 1 [10:181:1]
3136x (2 curves)	1	2- 7-	2- -1  3 7- -3  2 -3  1
Curve Equation t Generators 3136x1 [0,-1,0,-9,1] 1 [0:1:1] 3136x2 [0,-1,0,-569,-5039] 1 [-1680:13:125]
3136y (6 curves)	1	2- 7-	2-  2  0 7-  0 -4 -6 -2
Curve Equation t Generators 3136y1 [0,-1,0,-1633,51969] 2 [75:588:1] 3136y2 [0,-1,0,-32993,2316161] 2 [40:1029:1] 3136y3 [0,-1,0,14047,-1080127] 2 [136047:9658880:27] 3136y4 [0,-1,0,-111393,-11692351] 2 [-178376:1198785:1331] 3136y5 [0,-1,0,-534753,-150770815] 2 [336636235:8831271372:274625] 3136y6 [0,-1,0,-8562913,-9641661567] 2 [58225956563265465:3465439960080553532:10698900892875]
3136z (2 curves)	1	2- 7-	2-  2  0 7- -4 -4  2  6
Curve Equation t Generators 3136z1 [0,-1,0,327,-1735] 2 [23:132:1] 3136z2 [0,-1,0,-1633,-13887] 2 [117:1176:1]
3136ba (2 curves)	1	2- 7-	2- -2  0 7-  4 -4  2 -6
Curve Equation t Generators 3136ba1 [0,1,0,327,1735] 2 [2:49:1] 3136ba2 [0,1,0,-1633,13887] 2 [-19:196:1]
3136bb (2 curves)	1	2- 7-	2- -2 -4 7-  0  0  2  2
Curve Equation t Generators 3136bb1 [0,1,0,-65,-11201] 2 [37:196:1] 3136bb2 [0,1,0,-7905,-269921] 2 [-54:49:1]
3136bc (1 curve)	1	2- 7-	2- -3 -1 7- -1  2 -3 -5
Curve Equation t Generators 3136bc1 [0,0,0,-28,-56] 1 [-3:1:1]

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