Cremona's table of elliptic curves

12870 = 2 · 3² · 5 · 11 · 13

Class	r	Atkin-Lehner	Eigenvalues
12870a (1 curve)	0	2+ 3+ 5+ 11+ 13-	2+ 3+ 5+ -5 11+ 13-  0  1
Curve Equation t 12870a1 [1,-1,0,-11895,-498979] 1
12870b (2 curves)	1	2+ 3+ 5+ 11- 13-	2+ 3+ 5+  2 11- 13-  2  0
Curve Equation t Generators 12870b1 [1,-1,0,-15,2681] 2 [8:51:1] 12870b2 [1,-1,0,-2985,62675] 2 [-59:205:1]
12870c (4 curves)	1	2+ 3+ 5+ 11- 13-	2+ 3+ 5+  2 11- 13- -6  8
Curve Equation t Generators 12870c1 [1,-1,0,-7215,668781] 6 [33:666:1] 12870c2 [1,-1,0,-166935,26255925] 6 [-249:7359:1] 12870c3 [1,-1,0,63570,-16000300] 2 [25190:1404905:8] 12870c4 [1,-1,0,-696750,-198629164] 2 [237069294:12783652853:74088]
12870d (1 curve)	1	2+ 3+ 5+ 11- 13-	2+ 3+ 5+  3 11- 13- -8 -5
Curve Equation t Generators 12870d1 [1,-1,0,0,416] 1 [-5:19:1]
12870e (1 curve)	0	2+ 3+ 5- 11+ 13+	2+ 3+ 5-  1 11+ 13+ -4 -3
Curve Equation t 12870e1 [1,-1,0,1551,35783] 1
12870f (2 curves)	0	2+ 3+ 5- 11+ 13+	2+ 3+ 5- -2 11+ 13+  2  0
Curve Equation t 12870f1 [1,-1,0,-12489,-560755] 2 12870f2 [1,-1,0,-202569,-35041267] 2
12870g (2 curves)	1	2+ 3+ 5- 11+ 13-	2+ 3+ 5- -1 11+ 13-  0 -1
Curve Equation t Generators 12870g1 [1,-1,0,2074371,-344158065] 3 [1671:87402:1] 12870g2 [1,-1,0,-34253754,-79716579940] 1 [7471:281452:1]
12870h (2 curves)	1	2+ 3+ 5- 11+ 13-	2+ 3+ 5-  4 11+ 13-  0 -6
Curve Equation t Generators 12870h1 [1,-1,0,-879,10285] 2 [14:17:1] 12870h2 [1,-1,0,-14079,646525] 2 [59:107:1]
12870i (2 curves)	0	2+ 3+ 5- 11- 13-	2+ 3+ 5- -1 11- 13-  0  5
Curve Equation t 12870i1 [1,-1,0,-9984,11082240] 3 12870i2 [1,-1,0,89841,-298861075] 1
12870j (1 curve)	0	2+ 3- 5+ 11+ 13+	2+ 3- 5+ -1 11+ 13+  3  1
Curve Equation t 12870j1 [1,-1,0,-510,-4870] 1
12870k (6 curves)	1	2+ 3- 5+ 11+ 13-	2+ 3- 5+  0 11+ 13- -2  4
Curve Equation t Generators 12870k1 [1,-1,0,-25560,-679104] 2 [-63:855:1] 12870k2 [1,-1,0,-209880,36590400] 4 [-165:8250:1] 12870k3 [1,-1,0,-3346200,2356839936] 4 [813:12756:1] 12870k4 [1,-1,0,-22680,99377280] 2 [1161:39879:1] 12870k5 [1,-1,0,-53539200,150797618136] 2 [4245:159:1] 12870k6 [1,-1,0,-3334320,2374396200] 2 [1311:15315:1]
12870l (1 curve)	1	2+ 3- 5+ 11+ 13-	2+ 3- 5+ -3 11+ 13-  1 -5
Curve Equation t Generators 12870l1 [1,-1,0,-27510,-3571084] 1 [6275:493729:1]
12870m (4 curves)	0	2+ 3- 5+ 11- 13-	2+ 3- 5+  0 11- 13- -2  4
Curve Equation t 12870m1 [1,-1,0,-517920,-144501760] 2 12870m2 [1,-1,0,-8305440,-9210732544] 4 12870m3 [1,-1,0,-132887040,-589586574304] 2 12870m4 [1,-1,0,-8324160,-9167111200] 2
12870n (2 curves)	0	2+ 3- 5+ 11- 13-	2+ 3- 5+  4 11- 13-  2  0
Curve Equation t 12870n1 [1,-1,0,180,796] 2 12870n2 [1,-1,0,-990,8050] 2
12870o (4 curves)	0	2+ 3- 5+ 11- 13-	2+ 3- 5+  4 11- 13-  2  0
Curve Equation t 12870o1 [1,-1,0,-762194745,-8307793814675] 2 12870o2 [1,-1,0,-12282194745,-523913041814675] 4 12870o3 [1,-1,0,-196515074745,-33530596817126675] 2 12870o4 [1,-1,0,-12369314745,-516103378502675] 2
12870p (8 curves)	0	2+ 3- 5+ 11- 13-	2+ 3- 5+ -4 11- 13-  6 -4
Curve Equation t 12870p1 [1,-1,0,-102780,12157776] 2 12870p2 [1,-1,0,-287100,-43470000] 4 12870p3 [1,-1,0,-8224380,9080321616] 6 12870p4 [1,-1,0,-4247100,-3367494000] 2 12870p5 [1,-1,0,723780,-281835504] 2 12870p6 [1,-1,0,-8225100,9078652800] 12 12870p7 [1,-1,0,-9423000,6261910740] 6 12870p8 [1,-1,0,-7038720,11788581996] 6
12870q (4 curves)	2	2+ 3- 5+ 11- 13-	2+ 3- 5+ -4 11- 13- -6 -8
Curve Equation t Generators 12870q1 [1,-1,0,585,6925] 2 [-7:53:1]&[2:89:1] 12870q2 [1,-1,0,-3915,72625] 4 [-48:409:1]&[-40:425:1] 12870q3 [1,-1,0,-21465,-1145345] 2 [-79:269:1]&[-69:95:1] 12870q4 [1,-1,0,-58365,5441395] 2 [-103:3269:1]&[53:1553:1]
12870r (4 curves)	1	2+ 3- 5- 11+ 13+	2+ 3- 5-  0 11+ 13+  6  4
Curve Equation t Generators 12870r1 [1,-1,0,-414,-3132] 2 [-11:6:1] 12870r2 [1,-1,0,-594,0] 4 [-11:77:1] 12870r3 [1,-1,0,-6444,200070] 2 [69:249:1] 12870r4 [1,-1,0,2376,-1782] 2 [43:401:1]
12870s (2 curves)	1	2+ 3- 5- 11+ 13+	2+ 3- 5-  2 11+ 13+  4 -2
Curve Equation t Generators 12870s1 [1,-1,0,-9069669,10536334933] 2 [-478:121739:1] 12870s2 [1,-1,0,-145194669,673437859933] 2 [6947:-2011:1]
12870t (4 curves)	1	2+ 3- 5- 11+ 13+	2+ 3- 5- -4 11+ 13+ -2  4
Curve Equation t Generators 12870t1 [1,-1,0,-594,4180] 2 [29:89:1] 12870t2 [1,-1,0,-3474,-74732] 4 [-36:70:1] 12870t3 [1,-1,0,-54954,-4944740] 2 [-135:70:1] 12870t4 [1,-1,0,1926,-289652] 2 [99:880:1]
12870u (2 curves)	0	2+ 3- 5- 11+ 13-	2+ 3- 5- -2 11+ 13-  6 -4
Curve Equation t 12870u1 [1,-1,0,2691,-185787] 2 12870u2 [1,-1,0,-36909,-2490507] 2
12870v (2 curves)	0	2+ 3- 5- 11+ 13-	2+ 3- 5-  4 11+ 13-  6  0
Curve Equation t 12870v1 [1,-1,0,81261,-30817355] 2 12870v2 [1,-1,0,-1116819,-415880267] 2
12870w (4 curves)	0	2+ 3- 5- 11+ 13-	2+ 3- 5- -4 11+ 13-  6  8
Curve Equation t 12870w1 [1,-1,0,936,0] 2 12870w2 [1,-1,0,-3744,2808] 2 12870w3 [1,-1,0,-12924,607068] 6 12870w4 [1,-1,0,-210654,37266210] 6
12870x (4 curves)	1	2+ 3- 5- 11- 13-	2+ 3- 5-  0 11- 13- -6  4
Curve Equation t Generators 12870x1 [1,-1,0,9846,809460] 2 [21:1002:1] 12870x2 [1,-1,0,-93834,9580788] 4 [-123:4449:1] 12870x3 [1,-1,0,-402714,-88828380] 2 [-299:2337:1] 12870x4 [1,-1,0,-1443834,668110788] 4 [-483:35634:1]
12870y (1 curve)	1	2+ 3- 5- 11- 13-	2+ 3- 5-  1 11- 13-  5 -3
Curve Equation t Generators 12870y1 [1,-1,0,-8424,-295520] 1 [111:302:1]
12870z (2 curves)	1	2+ 3- 5- 11- 13-	2+ 3- 5- -2 11- 13-  2  0
Curve Equation t Generators 12870z1 [1,-1,0,-16434,825988] 2 [17:734:1] 12870z2 [1,-1,0,-263934,52256488] 2 [287:149:1]
12870ba (2 curves)	1	2+ 3- 5- 11- 13-	2+ 3- 5- -2 11- 13- -2  4
Curve Equation t Generators 12870ba1 [1,-1,0,-1404,-94640] 2 [104:884:1] 12870ba2 [1,-1,0,-41004,-3175520] 2 [-121:119:1]
12870bb (1 curve)	1	2+ 3- 5- 11- 13-	2+ 3- 5-  3 11- 13-  0 -5
Curve Equation t Generators 12870bb1 [1,-1,0,-54,-162] 1 [9:0:1]
12870bc (4 curves)	1	2+ 3- 5- 11- 13-	2+ 3- 5- -4 11- 13-  0  2
Curve Equation t Generators 12870bc1 [1,-1,0,7941861,159642619173] 2 [40686:4586127:8] 12870bc2 [1,-1,0,-397562139,2963216174373] 2 [76846014:609124663:5832] 12870bc3 [1,-1,0,-1996399899,34339915559205] 6 [8301:4278342:1] 12870bc4 [1,-1,0,-31943899899,2197513725059205] 6 [108301:2813357:1]
12870bd (2 curves)	1	2- 3+ 5+ 11+ 13-	2- 3+ 5+ -1 11+ 13-  0  5
Curve Equation t Generators 12870bd1 [1,-1,1,9982,11065601] 3 [-207:415:1] 12870bd2 [1,-1,1,-89858,-299130623] 1 [721:2879:1]
12870be (1 curve)	1	2- 3+ 5+ 11- 13+	2- 3+ 5+  1 11- 13+  4 -3
Curve Equation t Generators 12870be1 [1,-1,1,172,-1383] 1 [190:903:8]
12870bf (2 curves)	1	2- 3+ 5+ 11- 13+	2- 3+ 5+ -2 11- 13+ -2  0
Curve Equation t Generators 12870bf1 [1,-1,1,-1388,21231] 2 [5:117:1] 12870bf2 [1,-1,1,-22508,1305327] 2 [77:117:1]
12870bg (2 curves)	0	2- 3+ 5+ 11- 13-	2- 3+ 5+ -1 11- 13-  0 -1
Curve Equation t 12870bg1 [1,-1,1,-3805973,2953734581] 3 12870bg2 [1,-1,1,18669337,9273598417] 1
12870bh (2 curves)	0	2- 3+ 5+ 11- 13-	2- 3+ 5+  4 11- 13-  0 -6
Curve Equation t 12870bh1 [1,-1,1,-7913,-269783] 2 12870bh2 [1,-1,1,-126713,-17329463] 2
12870bi (2 curves)	0	2- 3+ 5- 11+ 13-	2- 3+ 5-  2 11+ 13- -2  0
Curve Equation t 12870bi1 [1,-1,1,-2,-99] 2 12870bi2 [1,-1,1,-332,-2211] 2
12870bj (4 curves)	0	2- 3+ 5- 11+ 13-	2- 3+ 5-  2 11+ 13-  6  8
Curve Equation t 12870bj1 [1,-1,1,7063,590249] 6 12870bj2 [1,-1,1,-77417,7382441] 6 12870bj3 [1,-1,1,-64937,-17992151] 2 12870bj4 [1,-1,1,-1502417,-707407559] 2
12870bk (1 curve)	0	2- 3+ 5- 11+ 13-	2- 3+ 5-  3 11+ 13-  8 -5
Curve Equation t 12870bk1 [1,-1,1,-2,-11231] 1
12870bl (1 curve)	1	2- 3+ 5- 11- 13-	2- 3+ 5- -5 11- 13-  0  1
Curve Equation t Generators 12870bl1 [1,-1,1,-1322,18921] 1 [11:69:1]
12870bm (2 curves)	1	2- 3- 5+ 11+ 13+	2- 3- 5+  2 11+ 13+ -4 -2
Curve Equation t Generators 12870bm1 [1,-1,1,668587,65772717] 2 [383:19248:1] 12870bm2 [1,-1,1,-2816213,541099437] 2 [-1453:40272:1]
12870bn (2 curves)	0	2- 3- 5+ 11+ 13-	2- 3- 5+  0 11+ 13-  4 -2
Curve Equation t 12870bn1 [1,-1,1,-6008,-239173] 2 12870bn2 [1,-1,1,-105008,-13069573] 2
12870bo (4 curves)	0	2- 3- 5+ 11- 13+	2- 3- 5+  0 11- 13+ -6  4
Curve Equation t 12870bo1 [1,-1,1,-1193,61017] 2 12870bo2 [1,-1,1,-31613,2166081] 4 12870bo3 [1,-1,1,-44483,245877] 2 12870bo4 [1,-1,1,-505463,138445341] 2
12870bp (1 curve)	0	2- 3- 5+ 11- 13+	2- 3- 5+  1 11- 13+  1  3
Curve Equation t 12870bp1 [1,-1,1,-9628403,27433323987] 1
12870bq (2 curves)	0	2- 3- 5+ 11- 13+	2- 3- 5+ -2 11- 13+  4  6
Curve Equation t 12870bq1 [1,-1,1,-391253,-134545719] 2 12870bq2 [1,-1,1,-6979703,-7094584299] 2
12870br (2 curves)	0	2- 3- 5+ 11- 13+	2- 3- 5+  4 11- 13+ -2  0
Curve Equation t 12870br1 [1,-1,1,-1238,-16923] 2 12870br2 [1,-1,1,-19958,-1080219] 2
12870bs (2 curves)	0	2- 3- 5+ 11- 13+	2- 3- 5+ -4 11- 13+ -4 -2
Curve Equation t 12870bs1 [1,-1,1,-1058,-42019] 2 12870bs2 [1,-1,1,-25808,-1586419] 2
12870bt (1 curve)	0	2- 3- 5+ 11- 13+	2- 3- 5+  5 11- 13+  4 -1
Curve Equation t 12870bt1 [1,-1,1,4702342,1889166777] 1
12870bu (2 curves)	1	2- 3- 5+ 11- 13-	2- 3- 5+ -1 11- 13-  0  5
Curve Equation t Generators 12870bu1 [1,-1,1,-743,67007] 1 [45:-374:1] 12870bu2 [1,-1,1,-149918,22380077] 3 [-135:6403:1]
12870bv (3 curves)	1	2- 3- 5+ 11- 13-	2- 3- 5+ -1 11- 13-  3 -7
Curve Equation t Generators 12870bv1 [1,-1,1,-4388,-156283] 1 [12893634:20029031:157464] 12870bv2 [1,-1,1,34987,2111717] 3 [505:11928:1] 12870bv3 [1,-1,1,-839588,299208647] 3 [-1055:3673:1]
12870bw (4 curves)	1	2- 3- 5+ 11- 13-	2- 3- 5+  2 11- 13- -6 -4
Curve Equation t Generators 12870bw1 [1,-1,1,-5378,1748081] 2 [63:1255:1] 12870bw2 [1,-1,1,-252878,48674081] 2 [-519:6577:1] 12870bw3 [1,-1,1,-1277753,556257881] 6 [-95:26062:1] 12870bw4 [1,-1,1,-20444153,35584770521] 6 [-1689:256372:1]
12870bx (4 curves)	0	2- 3- 5- 11+ 13+	2- 3- 5-  0 11+ 13+ -2 -4
Curve Equation t 12870bx1 [1,-1,1,-302,-25171] 2 12870bx2 [1,-1,1,-14882,-690019] 4 12870bx3 [1,-1,1,-237632,-44527219] 2 12870bx4 [1,-1,1,-25412,421949] 2
12870by (4 curves)	0	2- 3- 5- 11+ 13+	2- 3- 5-  0 11+ 13+ -6  0
Curve Equation t 12870by1 [1,-1,1,-15746117,-8802612291] 4 12870by2 [1,-1,1,-204489797,-1124579750979] 4 12870by3 [1,-1,1,-3271113797,-72008980186179] 2 12870by4 [1,-1,1,-157764677,-1652181115971] 2
12870bz (1 curve)	0	2- 3- 5- 11+ 13+	2- 3- 5-  5 11+ 13+  4 -5
Curve Equation t 12870bz1 [1,-1,1,463,2409] 1
12870ca (4 curves)	1	2- 3- 5- 11+ 13-	2- 3- 5-  0 11+ 13-  2 -4
Curve Equation t Generators 12870ca1 [1,-1,1,72733,28704291] 4 [-189:2954:1] 12870ca2 [1,-1,1,-1079267,398726691] 4 [-721:28674:1] 12870ca3 [1,-1,1,-3692867,-2274463389] 2 [-1081:21834:1] 12870ca4 [1,-1,1,-16897667,26739526371] 2 [2399:906:1]
12870cb (2 curves)	1	2- 3- 5- 11+ 13-	2- 3- 5- -1 11+ 13-  0 -7
Curve Equation t Generators 12870cb1 [1,-1,1,-36662,10594199] 1 [6846:193403:8] 12870cb2 [1,-1,1,-4968347,4263775571] 3 [1281:-236:1]
12870cc (1 curve)	1	2- 3- 5- 11+ 13-	2- 3- 5- -1 11+ 13- -5  3
Curve Equation t Generators 12870cc1 [1,-1,1,238,-111] 1 [9:47:1]
12870cd (4 curves)	1	2- 3- 5- 11+ 13-	2- 3- 5- -4 11+ 13- -2  0
Curve Equation t Generators 12870cd1 [1,-1,1,-22037,2963949] 4 [-163:1566:1] 12870cd2 [1,-1,1,-472037,124823949] 4 [-403:15996:1] 12870cd3 [1,-1,1,-593537,55666149] 2 [-433:15426:1] 12870cd4 [1,-1,1,-7550537,7987621749] 2 [1587:-774:1]
12870ce (1 curve)	1	2- 3- 5- 11- 13+	2- 3- 5-  1 11- 13+ -4  1
Curve Equation t Generators 12870ce1 [1,-1,1,89788,8603111] 1 [1701:-72131:1]
12870cf (4 curves)	0	2- 3- 5- 11- 13-	2- 3- 5-  4 11- 13- -6  4
Curve Equation t 12870cf1 [1,-1,1,193,58839] 4 12870cf2 [1,-1,1,-21587,1200111] 4 12870cf3 [1,-1,1,-48317,-2338941] 2 12870cf4 [1,-1,1,-343337,77519211] 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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