Cremona's table of elliptic curves

31122 = 2 · 3² · 7 · 13 · 19

Class	r	Atkin-Lehner	Eigenvalues
31122a (2 curves)	1	2+ 3+ 7+ 13+ 19+	2+ 3+ -2 7+ -4 13+  6 19+
Curve Equation t Generators 31122a1 [1,-1,0,-393,-1639] 2 [-16:27:1] 31122a2 [1,-1,0,-5523,-156565] 2 [-43:27:1]
31122b (2 curves)	1	2+ 3+ 7+ 13+ 19+	2+ 3+  4 7+  0 13+ -2 19+
Curve Equation t Generators 31122b1 [1,-1,0,-109905,13290893] 2 [7156:95377:64] 31122b2 [1,-1,0,85035,55202993] 2 [-226:5053:1]
31122c (2 curves)	2	2+ 3+ 7+ 13+ 19-	2+ 3+  0 7+ -4 13+  2 19-
Curve Equation t Generators 31122c1 [1,-1,0,-2037,35893] 2 [-49:152:1]&[23:17:1] 31122c2 [1,-1,0,-1797,44485] 2 [-46:191:1]&[-18:-257:1]
31122d (2 curves)	1	2+ 3+ 7+ 13- 19-	2+ 3+ -2 7+ -4 13- -2 19-
Curve Equation t Generators 31122d1 [1,-1,0,-123513,-16653511] 2 [-202:253:1] 31122d2 [1,-1,0,-1975443,-1068179365] 2 [13166:86783:8]
31122e (2 curves)	0	2+ 3+ 7- 13+ 19+	2+ 3+  4 7-  0 13+  6 19+
Curve Equation t 31122e1 [1,-1,0,-100590,-11514412] 2 31122e2 [1,-1,0,-1582350,-765730252] 2
31122f (2 curves)	1	2+ 3+ 7- 13- 19+	2+ 3+  0 7- -4 13-  2 19+
Curve Equation t Generators 31122f1 [1,-1,0,-1932,32732] 2 [1:175:1] 31122f2 [1,-1,0,-3822,-40222] 2 [-13:91:1]
31122g (2 curves)	0	2+ 3+ 7- 13- 19-	2+ 3+  4 7- -4 13- -2 19-
Curve Equation t 31122g1 [1,-1,0,-91260,-1012912] 2 31122g2 [1,-1,0,-951420,355953488] 2
31122h (1 curve)	1	2+ 3- 7+ 13- 19+	2+ 3- -1 7+ -3 13-  6 19+
Curve Equation t Generators 31122h1 [1,-1,0,0,-108] 1 [6:6:1]
31122i (4 curves)	1	2+ 3- 7+ 13- 19+	2+ 3-  2 7+  0 13- -6 19+
Curve Equation t Generators 31122i1 [1,-1,0,-35316,2484432] 2 [184:1388:1] 31122i2 [1,-1,0,-560196,161523072] 4 [189:7803:1] 31122i3 [1,-1,0,-555336,164459484] 2 [310:-4848:1] 31122i4 [1,-1,0,-8963136,10330761060] 4 [1458:18252:1]
31122j (1 curve)	1	2+ 3- 7+ 13- 19+	2+ 3- -3 7+  5 13-  0 19+
Curve Equation t Generators 31122j1 [1,-1,0,3159,14413] 1 [2:143:1]
31122k (2 curves)	2	2+ 3- 7+ 13- 19-	2+ 3- -2 7+ -6 13-  0 19-
Curve Equation t Generators 31122k1 [1,-1,0,-288,1840] 2 [-19:23:1]&[-4:56:1] 31122k2 [1,-1,0,252,7564] 2 [-10:-58:1]&[-12:58:1]
31122l (4 curves)	2	2+ 3- 7- 13+ 19-	2+ 3- -2 7- -4 13+ -6 19-
Curve Equation t Generators 31122l1 [1,-1,0,-15993,782365] 2 [-118:1067:1]&[-34:1151:1] 31122l2 [1,-1,0,-17613,615505] 4 [152:-1273:1]&[-114:1121:1] 31122l3 [1,-1,0,49077,4123399] 2 [35:-2443:1]&[-210:13531:8] 31122l4 [1,-1,0,-110223,-13590869] 2 [-205:701:1]&[-163:239:1]
31122m (6 curves)	1	2+ 3- 7- 13- 19-	2+ 3-  0 7-  0 13- -6 19-
Curve Equation t Generators 31122m1 [1,-1,0,-306657,-63059715] 2 [-17580:48885:64] 31122m2 [1,-1,0,131103,-228795651] 2 [147224580:19901660577:8000] 31122m3 [1,-1,0,-3650337,2665989693] 6 [-57:53637:1] 31122m4 [1,-1,0,-1181097,6211324485] 6 [-1983:28428:1] 31122m5 [1,-1,0,-295085637,1951131954177] 6 [9771:20409:1] 31122m6 [1,-1,0,-295083927,1951155696843] 6 [3352251:7137201:343]
31122n (1 curve)	1	2+ 3- 7- 13- 19-	2+ 3-  1 7- -1 13-  4 19-
Curve Equation t Generators 31122n1 [1,-1,0,-3759,-97363] 1 [238:3409:1]
31122o (3 curves)	1	2+ 3- 7- 13- 19-	2+ 3-  3 7-  3 13- -6 19-
Curve Equation t Generators 31122o1 [1,-1,0,-288,-27648] 1 [6720:38112:125] 31122o2 [1,-1,0,2592,744768] 3 [96:1320:1] 31122o3 [1,-1,0,-548028,156321252] 3 [432:18:1]
31122p (2 curves)	0	2- 3+ 7+ 13+ 19+	2- 3+  2 7+  4 13+ -6 19+
Curve Equation t 31122p1 [1,-1,1,-44,75] 2 31122p2 [1,-1,1,-614,6003] 2
31122q (2 curves)	0	2- 3+ 7+ 13+ 19+	2- 3+ -4 7+  0 13+  2 19+
Curve Equation t 31122q1 [1,-1,1,-12212,-488185] 2 31122q2 [1,-1,1,9448,-2047705] 2
31122r (2 curves)	1	2- 3+ 7+ 13+ 19-	2- 3+  0 7+  4 13+ -2 19-
Curve Equation t Generators 31122r1 [1,-1,1,-18335,-950777] 2 [179:1126:1] 31122r2 [1,-1,1,-16175,-1184921] 2 [283:3962:1]
31122s (2 curves)	0	2- 3+ 7+ 13- 19-	2- 3+  2 7+  4 13-  2 19-
Curve Equation t 31122s1 [1,-1,1,-13724,621371] 2 31122s2 [1,-1,1,-219494,39635363] 2
31122t (2 curves)	1	2- 3+ 7- 13+ 19+	2- 3+ -4 7-  0 13+ -6 19+
Curve Equation t Generators 31122t1 [1,-1,1,-11177,430185] 2 [173:1824:1] 31122t2 [1,-1,1,-175817,28418985] 2 [257:-528:1]
31122u (2 curves)	0	2- 3+ 7- 13- 19+	2- 3+  0 7-  4 13- -2 19+
Curve Equation t 31122u1 [1,-1,1,-215,-1141] 2 31122u2 [1,-1,1,-425,1631] 2
31122v (2 curves)	1	2- 3+ 7- 13- 19-	2- 3+ -4 7-  4 13-  2 19-
Curve Equation t Generators 31122v1 [1,-1,1,-821342,28169965] 2 [-839:11651:1] 31122v2 [1,-1,1,-8562782,-9602181395] 2 [-1735:6275:1]
31122w (4 curves)	1	2- 3- 7+ 13+ 19+	2- 3-  2 7+  0 13+ -2 19+
Curve Equation t Generators 31122w1 [1,-1,1,-9482639,11241735383] 2 [1011:51334:1] 31122w2 [1,-1,1,-9528719,11126996183] 4 [-213:114766:1] 31122w3 [1,-1,1,348241,33065699735] 2 [110555:23015526:125] 31122w4 [1,-1,1,-20142959,-18155569129] 2 [-1185:64222:1]
31122x (2 curves)	1	2- 3- 7+ 13+ 19+	2- 3-  2 7+ -2 13+  0 19+
Curve Equation t Generators 31122x1 [1,-1,1,-15584,-739965] 2 [-75:89:1] 31122x2 [1,-1,1,-5504,-1691517] 2 [177:1601:1]
31122y (1 curve)	0	2- 3- 7+ 13+ 19-	2- 3-  1 7+  5 13+  4 19-
Curve Equation t 31122y1 [1,-1,1,266443,205900237] 1
31122z (2 curves)	0	2- 3- 7+ 13- 19+	2- 3- -2 7+ -2 13- -8 19+
Curve Equation t 31122z1 [1,-1,1,-649976,-201525033] 2 31122z2 [1,-1,1,-619106,-221553489] 2
31122ba (2 curves)	1	2- 3- 7+ 13- 19-	2- 3- -4 7+ -4 13- -2 19-
Curve Equation t Generators 31122ba1 [1,-1,1,-6827,-133765] 2 [-33:-218:1] 31122ba2 [1,-1,1,20533,-954565] 2 [423:-9338:1]
31122bb (2 curves)	0	2- 3- 7- 13+ 19+	2- 3-  2 7- -2 13+  8 19+
Curve Equation t 31122bb1 [1,-1,1,-52484,-4583257] 2 31122bb2 [1,-1,1,-17924,-10555225] 2
31122bc (1 curve)	1	2- 3- 7- 13- 19+	2- 3-  0 7-  1 13- -2 19+
Curve Equation t Generators 31122bc1 [1,-1,1,-4370,-112111] 1 [97:559:1]
31122bd (3 curves)	0	2- 3- 7- 13- 19-	2- 3-  0 7- -3 13-  6 19-
Curve Equation t 31122bd1 [1,-1,1,-7835,-840895] 1 31122bd2 [1,-1,1,69340,20700191] 3 31122bd3 [1,-1,1,-4138115,3244656899] 3
31122be (2 curves)	0	2- 3- 7- 13- 19-	2- 3-  3 7-  3 13-  0 19-
Curve Equation t 31122be1 [1,-1,1,-387851,-95204437] 1 31122be2 [1,-1,1,1759054,-370202191] 3
31122bf (2 curves)	0	2- 3- 7- 13- 19-	2- 3- -4 7-  0 13- -2 19-
Curve Equation t 31122bf1 [1,-1,1,-347,-345] 2 31122bf2 [1,-1,1,1363,-3765] 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
Back to Tables and computations