Cremona's table of elliptic curves

52080 = 2⁴ · 3 · 5 · 7 · 31

Class	r	Atkin-Lehner	Eigenvalues
52080a (1 curve)	1	2+ 3+ 5+ 7+ 31+	2+ 3+ 5+ 7+  2  3 -1  5
Curve Equation t Generators 52080a1 [0,-1,0,-1856,154656] 1 [-62:166:1]
52080b (4 curves)	2	2+ 3+ 5+ 7- 31+	2+ 3+ 5+ 7-  0 -2 -2 -4
Curve Equation t Generators 52080b1 [0,-1,0,-1036,24160] 2 [-15:190:1]&[-4:168:1] 52080b2 [0,-1,0,-20256,1115856] 4 [858:-3255:8]&[-66:1470:1] 52080b3 [0,-1,0,-23976,681360] 2 [176:-1372:1]&[-46:1298:1] 52080b4 [0,-1,0,-324056,71111376] 2 [333:126:1]&[410:2646:1]
52080c (4 curves)	0	2+ 3+ 5+ 7- 31+	2+ 3+ 5+ 7-  4  2  2  4
Curve Equation t 52080c1 [0,-1,0,9,3066] 2 52080c2 [0,-1,0,-3116,66816] 4 52080c3 [0,-1,0,-6616,-106784] 2 52080c4 [0,-1,0,-49616,4270416] 4
52080d (2 curves)	2	2+ 3+ 5+ 7- 31+	2+ 3+ 5+ 7- -6  2  0 -8
Curve Equation t Generators 52080d1 [0,-1,0,184,18816] 2 [-19:90:1]&[-10:126:1] 52080d2 [0,-1,0,-9616,355936] 2 [-75:806:1]&[18:434:1]
52080e (1 curve)	1	2+ 3+ 5+ 7- 31-	2+ 3+ 5+ 7-  4  3 -5 -1
Curve Equation t Generators 52080e1 [0,-1,0,-94256,18040800] 1 [106:-3038:1]
52080f (2 curves)	0	2+ 3+ 5- 7+ 31+	2+ 3+ 5- 7+  0  2  6  2
Curve Equation t 52080f1 [0,-1,0,-1800,-28800] 2 52080f2 [0,-1,0,-1680,-32928] 2
52080g (6 curves)	0	2+ 3+ 5- 7+ 31+	2+ 3+ 5- 7+ -4  6  2 -4
Curve Equation t 52080g1 [0,-1,0,-473215,-5052938] 2 52080g2 [0,-1,0,-5090820,4407530400] 4 52080g3 [0,-1,0,-2688320,8576348400] 2 52080g4 [0,-1,0,-81375000,282570164352] 8 52080g5 [0,-1,0,-81296880,283139690400] 4 52080g6 [0,-1,0,-1302000000,18083188664352] 4
52080h (4 curves)	0	2+ 3- 5+ 7+ 31+	2+ 3- 5+ 7+  0 -2  2  4
Curve Equation t 52080h1 [0,1,0,34929,2493504] 2 52080h2 [0,1,0,-200516,23401020] 4 52080h3 [0,1,0,-1255136,-523735836] 2 52080h4 [0,1,0,-2913016,1912386020] 4
52080i (2 curves)	0	2+ 3- 5+ 7+ 31+	2+ 3- 5+ 7+ -2  2  4  0
Curve Equation t 52080i1 [0,1,0,396024,353563524] 2 52080i2 [0,1,0,-5728976,4859113524] 2
52080j (4 curves)	1	2+ 3- 5+ 7+ 31-	2+ 3- 5+ 7+ -4 -2  2 -4
Curve Equation t Generators 52080j1 [0,1,0,-7596,252300] 2 [59:114:1] 52080j2 [0,1,0,-7616,250884] 4 [-8:558:1] 52080j3 [0,1,0,-1736,634260] 2 [186:-2604:1] 52080j4 [0,1,0,-13816,-222796] 2 [-28:378:1]
52080k (2 curves)	1	2+ 3- 5+ 7+ 31-	2+ 3- 5+ 7+ -6  0 -4 -4
Curve Equation t Generators 52080k1 [0,1,0,-10596,-538020] 2 [147:1050:1] 52080k2 [0,1,0,-182096,-29967420] 2 [-248:30:1]
52080l (1 curve)	1	2+ 3- 5+ 7- 31+	2+ 3- 5+ 7-  2  1 -5  5
Curve Equation t Generators 52080l1 [0,1,0,-26976,1696404] 1 [92:42:1]
52080m (2 curves)	1	2+ 3- 5+ 7- 31+	2+ 3- 5+ 7-  2  4 -8 -4
Curve Equation t Generators 52080m1 [0,1,0,604,3804] 2 [19:150:1] 52080m2 [0,1,0,-2896,30404] 2 [-16:270:1]
52080n (2 curves)	0	2+ 3- 5+ 7- 31-	2+ 3- 5+ 7-  0  0 -6 -8
Curve Equation t 52080n1 [0,1,0,-1457496,-679064796] 2 52080n2 [0,1,0,-23332496,-43387814796] 2
52080o (4 curves)	0	2+ 3- 5+ 7- 31-	2+ 3- 5+ 7-  0  6  2  0
Curve Equation t 52080o1 [0,1,0,-16276,-804676] 2 52080o2 [0,1,0,-16296,-802620] 4 52080o3 [0,1,0,-7616,-1646316] 2 52080o4 [0,1,0,-25296,172980] 4
52080p (4 curves)	1	2+ 3- 5- 7+ 31+	2+ 3- 5- 7+ -4 -2 -2 -4
Curve Equation t Generators 52080p1 [0,1,0,-767095,-261157732] 2 [24467216:1869574665:4096] 52080p2 [0,1,0,-12303900,-16615732500] 4 [5910:342240:1] 52080p3 [0,1,0,-12334280,-16529586972] 4 [-1949:10500:1] 52080p4 [0,1,0,-196862400,-1063210074300] 2 [25755:3309240:1]
52080q (2 curves)	1	2+ 3- 5- 7+ 31+	2+ 3- 5- 7+ -4  4 -2 -4
Curve Equation t Generators 52080q1 [0,1,0,0,900] 2 [0:-30:1] 52080q2 [0,1,0,-1400,19380] 2 [-12:186:1]
52080r (4 curves)	0	2+ 3- 5- 7+ 31-	2+ 3- 5- 7+  4 -6 -6  4
Curve Equation t 52080r1 [0,1,0,-1540,-28612] 2 52080r2 [0,1,0,-26040,-1626012] 4 52080r3 [0,1,0,-27440,-1442892] 4 52080r4 [0,1,0,-416640,-103650732] 2
52080s (1 curve)	0	2+ 3- 5- 7- 31+	2+ 3- 5- 7-  0  5 -5 -1
Curve Equation t 52080s1 [0,1,0,-40,-172] 1
52080t (4 curves)	0	2+ 3- 5- 7- 31+	2+ 3- 5- 7-  4  6  6 -4
Curve Equation t 52080t1 [0,1,0,905,-3700] 2 52080t2 [0,1,0,-3900,-34452] 4 52080t3 [0,1,0,-34280,2408100] 4 52080t4 [0,1,0,-50400,-4368252] 2
52080u (4 curves)	1	2+ 3- 5- 7- 31-	2+ 3- 5- 7-  0 -2 -2 -4
Curve Equation t Generators 52080u1 [0,1,0,5065900,-55199781252] 2 [5866:420000:1] 52080u2 [0,1,0,-190246600,-975746656252] 4 [-8434:170100:1] 52080u3 [0,1,0,-490371600,2861891693748] 4 [-21909:1757700:1] 52080u4 [0,1,0,-3015121600,-63725260006252] 2 [-31684:-7350:1]
52080v (2 curves)	2	2- 3+ 5+ 7+ 31+	2- 3+ 5+ 7+  2 -6 -8  0
Curve Equation t Generators 52080v1 [0,-1,0,-99456,-45158400] 2 [458:2270:1]&[546:7938:1] 52080v2 [0,-1,0,-2608256,-1616670720] 2 [-926:1922:1]&[-896:448:1]
52080w (2 curves)	0	2- 3+ 5+ 7+ 31+	2- 3+ 5+ 7+  4 -2  0  4
Curve Equation t 52080w1 [0,-1,0,1519,0] 2 52080w2 [0,-1,0,-6076,6076] 2
52080x (2 curves)	2	2- 3+ 5+ 7+ 31+	2- 3+ 5+ 7+ -4 -6 -2  6
Curve Equation t Generators 52080x1 [0,-1,0,-1776,29376] 2 [-30:234:1]&[-24:240:1] 52080x2 [0,-1,0,-1296,45120] 2 [-22:250:1]&[-16:248:1]
52080y (2 curves)	0	2- 3+ 5+ 7+ 31+	2- 3+ 5+ 7+  6 -1  3  1
Curve Equation t 52080y1 [0,-1,0,-135401616,-644759922240] 1 52080y2 [0,-1,0,781682544,-402725127744] 1
52080z (1 curve)	1	2- 3+ 5+ 7+ 31-	2- 3+ 5+ 7+  2 -5  3 -1
Curve Equation t Generators 52080z1 [0,-1,0,-3816,520560] 1 [26:662:1]
52080ba (2 curves)	1	2- 3+ 5+ 7+ 31-	2- 3+ 5+ 7+ -4 -2 -6  2
Curve Equation t Generators 52080ba1 [0,-1,0,-44056,-3536144] 2 [396:6400:1] 52080ba2 [0,-1,0,-26776,-6356240] 2 [1101:36022:1]
52080bb (1 curve)	1	2- 3+ 5+ 7- 31+	2- 3+ 5+ 7-  0 -5  3 -3
Curve Equation t Generators 52080bb1 [0,-1,0,-7896,679920] 1 [146:1618:1]
52080bc (4 curves)	2	2- 3+ 5+ 7- 31-	2- 3+ 5+ 7-  0 -2 -6 -4
Curve Equation t Generators 52080bc1 [0,-1,0,-2576,-37440] 2 [-31:108:1]&[-22:90:1] 52080bc2 [0,-1,0,-14096,616896] 4 [-94:1050:1]&[-40:1056:1] 52080bc3 [0,-1,0,9904,2479296] 4 [-104:560:1]&[-62:1274:1] 52080bc4 [0,-1,0,-222416,40447680] 2 [274:38:1]&[394:3718:1]
52080bd (2 curves)	0	2- 3+ 5+ 7- 31-	2- 3+ 5+ 7-  4  0  6  8
Curve Equation t 52080bd1 [0,-1,0,-5136,-221760] 2 52080bd2 [0,-1,0,-94736,-11188800] 2
52080be (2 curves)	1	2- 3+ 5- 7+ 31+	2- 3+ 5- 7+  0 -1  3  7
Curve Equation t Generators 52080be1 [0,-1,0,-6200,-186000] 1 [130:1090:1] 52080be2 [0,-1,0,7000,-834960] 1 [559946:5875754:4913]
52080bf (4 curves)	1	2- 3+ 5- 7+ 31+	2- 3+ 5- 7+  0  2  6 -2
Curve Equation t Generators 52080bf1 [0,-1,0,-1056480,410902272] 2 [474:4050:1] 52080bf2 [0,-1,0,49440,1227513600] 2 [-880:22400:1] 52080bf3 [0,-1,0,-85152480,302471753472] 2 [6928:212160:1] 52080bf4 [0,-1,0,-85150560,302486073600] 2 [-2080:686000:1]
52080bg (4 curves)	1	2- 3+ 5- 7+ 31+	2- 3+ 5- 7+  0 -4 -6  4
Curve Equation t Generators 52080bg1 [0,-1,0,-1800,-810000] 2 [180:-2160:1] 52080bg2 [0,-1,0,-141800,-20298000] 2 [-230:310:1] 52080bg3 [0,-1,0,16200,21855600] 2 [60:4800:1] 52080bg4 [0,-1,0,-1081400,422260080] 2 [746:5490:1]
52080bh (1 curve)	0	2- 3+ 5- 7+ 31-	2- 3+ 5- 7+  4 -5 -5  5
Curve Equation t 52080bh1 [0,-1,0,-215440,-53710400] 1
52080bi (6 curves)	0	2- 3+ 5- 7+ 31-	2- 3+ 5- 7+ -4  6  2 -4
Curve Equation t 52080bi1 [0,-1,0,-10480,-739328] 2 52080bi2 [0,-1,0,-202560,-35006400] 4 52080bi3 [0,-1,0,-237840,-21938688] 8 52080bi4 [0,-1,0,-3240560,-2244240000] 2 52080bi5 [0,-1,0,812160,-163898688] 4 52080bi6 [0,-1,0,-1852320,955790400] 4
52080bj (2 curves)	2	2- 3+ 5- 7+ 31-	2- 3+ 5- 7+ -6  0 -4 -4
Curve Equation t Generators 52080bj1 [0,-1,0,66040,2425392] 2 [-28:744:1]&[964:31000:1] 52080bj2 [0,-1,0,-283960,20345392] 2 [-206:8370:1]&[-51:5890:1]
52080bk (2 curves)	0	2- 3+ 5- 7- 31+	2- 3+ 5- 7-  0  6 -8  4
Curve Equation t 52080bk1 [0,-1,0,-6585,3357900] 2 52080bk2 [0,-1,0,-378740,89102412] 2
52080bl (4 curves)	0	2- 3+ 5- 7- 31+	2- 3+ 5- 7-  0 -6 -2  4
Curve Equation t 52080bl1 [0,-1,0,-756400,120280000] 2 52080bl2 [0,-1,0,-5999280,-5571390528] 4 52080bl3 [0,-1,0,-285360,-15751310400] 4 52080bl4 [0,-1,0,-95599280,-359742270528] 2
52080bm (1 curve)	0	2- 3+ 5- 7- 31+	2- 3+ 5- 7-  6  3 -5  7
Curve Equation t 52080bm1 [0,-1,0,800,1792] 1
52080bn (4 curves)	1	2- 3+ 5- 7- 31-	2- 3+ 5- 7-  0  6 -2  4
Curve Equation t Generators 52080bn1 [0,-1,0,-292320,90968832] 2 [594:-11250:1] 52080bn2 [0,-1,0,-5292320,4686968832] 4 [-206:75950:1] 52080bn3 [0,-1,0,-5912320,3520872832] 2 [-286:72030:1] 52080bn4 [0,-1,0,-84672320,299917064832] 4 [3329:234360:1]
52080bo (1 curve)	1	2- 3+ 5- 7- 31-	2- 3+ 5- 7- -2 -1 -1  5
Curve Equation t Generators 52080bo1 [0,-1,0,440,7792] 1 [-6:70:1]
52080bp (6 curves)	1	2- 3+ 5- 7- 31-	2- 3+ 5- 7- -4 -2 -6 -4
Curve Equation t Generators 52080bp1 [0,-1,0,-12320,-10809600] 2 [290:3150:1] 52080bp2 [0,-1,0,-812320,-278969600] 4 [-528:1568:1] 52080bp3 [0,-1,0,-1460320,229580800] 8 [-560:29520:1] 52080bp4 [0,-1,0,-12964320,-17962560000] 2 [-2078:18:1] 52080bp5 [0,-1,0,5458880,1773946240] 4 [1362:108322:1] 52080bp6 [0,-1,0,-18747520,31222072960] 4 [1786:58590:1]
52080bq (2 curves)	0	2- 3- 5+ 7- 31+	2- 3- 5+ 7- -2  2  4  8
Curve Equation t 52080bq1 [0,1,0,-208517216,13827816468084] 2 52080bq2 [0,1,0,-10008517216,382695896468084] 2
52080br (1 curve)	0	2- 3- 5+ 7- 31+	2- 3- 5+ 7- -2 -3 -1 -7
Curve Equation t 52080br1 [0,1,0,-2576,-60396] 1
52080bs (4 curves)	0	2- 3- 5+ 7- 31+	2- 3- 5+ 7-  4  2 -2 -4
Curve Equation t 52080bs1 [0,1,0,-14096,-381420] 2 52080bs2 [0,1,0,-198416,-34075116] 4 52080bs3 [0,1,0,-171536,-43612140] 2 52080bs4 [0,1,0,-3174416,-2177985516] 2
52080bt (4 curves)	0	2- 3- 5+ 7- 31+	2- 3- 5+ 7-  4 -6  2  8
Curve Equation t 52080bt1 [0,1,0,744,8340] 2 52080bt2 [0,1,0,-4376,75924] 4 52080bt3 [0,1,0,-26776,-1635436] 2 52080bt4 [0,1,0,-63896,6194580] 2
52080bu (4 curves)	2	2- 3- 5+ 7- 31+	2- 3- 5+ 7- -4 -6 -2 -4
Curve Equation t Generators 52080bu1 [0,1,0,-92496,10734804] 2 [204:-630:1]&[-300:3402:1] 52080bu2 [0,1,0,-150816,-4498380] 4 [852:-22050:1]&[-324:3234:1] 52080bu3 [0,1,0,590064,-35022636] 2 [684:-26250:1]&[180:8778:1] 52080bu4 [0,1,0,-1824816,-947964780] 2 [-798:840:1]&[2282:82320:1]
52080bv (2 curves)	1	2- 3- 5+ 7- 31-	2- 3- 5+ 7-  0  4 -6  0
Curve Equation t Generators 52080bv1 [0,1,0,49504,-2155020] 2 [532:-13230:1] 52080bv2 [0,1,0,-224896,-18509260] 2 [-364:3906:1]
52080bw (1 curve)	1	2- 3- 5+ 7- 31-	2- 3- 5+ 7- -2  1  3  3
Curve Equation t Generators 52080bw1 [0,1,0,-14056,669620] 1 [164:1674:1]
52080bx (1 curve)	0	2- 3- 5- 7+ 31+	2- 3- 5- 7+  6 -7  7 -1
Curve Equation t 52080bx1 [0,1,0,-13193600,-18505554252] 1
52080by (2 curves)	1	2- 3- 5- 7+ 31-	2- 3- 5- 7+  2  4  4 -4
Curve Equation t Generators 52080by1 [0,1,0,3800,312500] 2 [20:-630:1] 52080by2 [0,1,0,-52200,4187700] 2 [-180:2790:1]
52080bz (6 curves)	1	2- 3- 5- 7+ 31-	2- 3- 5- 7+  4 -2 -6 -4
Curve Equation t Generators 52080bz1 [0,1,0,318240,-130985100] 2 [570:15360:1] 52080bz2 [0,1,0,-2755040,-1484457612] 4 [-1094:14880:1] 52080bz3 [0,1,0,-12555040,15712582388] 8 [986:65520:1] 52080bz4 [0,1,0,-42127520,-105254565900] 2 [-3740:1650:1] 52080bz5 [0,1,0,14352960,73973783988] 4 [10596:1189890:1] 52080bz6 [0,1,0,-196263040,1058218740788] 4 [8276:29250:1]
52080ca (2 curves)	1	2- 3- 5- 7+ 31-	2- 3- 5- 7+ -4 -2  2 -2
Curve Equation t Generators 52080ca1 [0,1,0,-1364560,-366952300] 2 [-772:15066:1] 52080ca2 [0,1,0,4234160,-2604200812] 2 [7298:645792:1]
52080cb (4 curves)	1	2- 3- 5- 7- 31+	2- 3- 5- 7-  0  2 -2  4
Curve Equation t Generators 52080cb1 [0,1,0,-2240,35700] 2 [-20:270:1] 52080cb2 [0,1,0,-8720,-277932] 4 [-62:168:1] 52080cb3 [0,1,0,13600,-1447500] 4 [124:1470:1] 52080cb4 [0,1,0,-134720,-19077132] 2 [-212:18:1]
52080cc (2 curves)	1	2- 3- 5- 7- 31+	2- 3- 5- 7- -2  0 -4 -4
Curve Equation t Generators 52080cc1 [0,1,0,-1135800,475980948] 2 [516:-5250:1] 52080cc2 [0,1,0,-18285800,30090600948] 2 [2476:-630:1]
52080cd (2 curves)	1	2- 3- 5- 7- 31+	2- 3- 5- 7- -2  4 -4  4
Curve Equation t Generators 52080cd1 [0,1,0,-3640,-93100] 2 [140:1470:1] 52080cd2 [0,1,0,-59640,-5625900] 2 [300:1890:1]
52080ce (1 curve)	1	2- 3- 5- 7- 31+	2- 3- 5- 7-  4  1 -1 -5
Curve Equation t Generators 52080ce1 [0,1,0,961960,526071828] 1 [1468:71442:1]
52080cf (6 curves)	1	2- 3- 5- 7- 31+	2- 3- 5- 7- -4 -2 -6 -4
Curve Equation t Generators 52080cf1 [0,1,0,-302720,-64208652] 2 [3778:229632:1] 52080cf2 [0,1,0,-302800,-64173100] 4 [-325:120:1] 52080cf3 [0,1,0,-227200,-96923020] 2 [683:8184:1] 52080cf4 [0,1,0,-379680,-29146572] 8 [-564:2430:1] 52080cf5 [0,1,0,1428240,-225125100] 4 [330:-16800:1] 52080cf6 [0,1,0,-3417680,2409759828] 4 [1156:2250:1]
52080cg (4 curves)	0	2- 3- 5- 7- 31-	2- 3- 5- 7-  0 -2  6  4
Curve Equation t 52080cg1 [0,1,0,-95520,-29925900] 2 52080cg2 [0,1,0,-2143520,-1207116300] 4 52080cg3 [0,1,0,-2770720,-443688460] 4 52080cg4 [0,1,0,-34284320,-77277961740] 2

Data from Elliptic Curve Data by J. E. Cremona.
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Part of Computational Number Theory
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