Cremona's table of elliptic curves

42840 = 2³ · 3² · 5 · 7 · 17

Class	r	Atkin-Lehner	Eigenvalues
42840a (2 curves)	0	2+ 3+ 5+ 7+ 17-	2+ 3+ 5+ 7+ -2 -2 17-  0
Curve Equation t 42840a1 [0,0,0,-68823,-58550742] 2 42840a2 [0,0,0,-2721843,-1718810658] 2
42840b (2 curves)	2	2+ 3+ 5+ 7- 17+	2+ 3+ 5+ 7- -4 -4 17+ -4
Curve Equation t Generators 42840b1 [0,0,0,-258,257] 2 [-16:17:1]&[-11:42:1] 42840b2 [0,0,0,1017,2042] 2 [-1:32:1]&[19:168:1]
42840c (2 curves)	1	2+ 3+ 5+ 7- 17-	2+ 3+ 5+ 7-  0 -4 17-  8
Curve Equation t Generators 42840c1 [0,0,0,57,-198] 2 [19:88:1] 42840c2 [0,0,0,-363,-1962] 2 [-9:24:1]
42840d (2 curves)	0	2+ 3+ 5- 7+ 17+	2+ 3+ 5- 7+  6 -2 17+ -4
Curve Equation t 42840d1 [0,0,0,1593,15066] 2 42840d2 [0,0,0,-7587,130734] 2
42840e (4 curves)	0	2+ 3- 5+ 7+ 17+	2+ 3- 5+ 7+  0  2 17+  0
Curve Equation t 42840e1 [0,0,0,21417,-413782] 2 42840e2 [0,0,0,-91083,-3406282] 4 42840e3 [0,0,0,-820083,283382318] 2 42840e4 [0,0,0,-1162083,-481714882] 2
42840f (4 curves)	0	2+ 3- 5+ 7+ 17+	2+ 3- 5+ 7+  0 -2 17+  4
Curve Equation t 42840f1 [0,0,0,-2343,-67142] 2 42840f2 [0,0,0,-42843,-3412442] 4 42840f3 [0,0,0,-48243,-2497682] 2 42840f4 [0,0,0,-685443,-218426402] 2
42840g (2 curves)	0	2+ 3- 5+ 7+ 17+	2+ 3- 5+ 7+  2  4 17+  8
Curve Equation t 42840g1 [0,0,0,-5358,127073] 2 42840g2 [0,0,0,-81903,9021602] 2
42840h (1 curve)	0	2+ 3- 5+ 7+ 17+	2+ 3- 5+ 7+  2  7 17+ -2
Curve Equation t 42840h1 [0,0,0,-16068,-784348] 1
42840i (2 curves)	2	2+ 3- 5+ 7+ 17+	2+ 3- 5+ 7+ -2  0 17+ -8
Curve Equation t Generators 42840i1 [0,0,0,-11478,128977] 2 [-91:648:1]&[-52:765:1] 42840i2 [0,0,0,-107103,-13392398] 2 [-181:252:1]&[-177:140:1]
42840j (2 curves)	0	2+ 3- 5+ 7+ 17+	2+ 3- 5+ 7+ -2  4 17+ -4
Curve Equation t 42840j1 [0,0,0,-159438,-24471263] 2 42840j2 [0,0,0,-2550063,-1567380638] 2
42840k (6 curves)	0	2+ 3- 5+ 7+ 17+	2+ 3- 5+ 7+  4 -2 17+ -4
Curve Equation t 42840k1 [0,0,0,10662,3402457] 2 42840k2 [0,0,0,-284583,55897018] 4 42840k3 [0,0,0,-794883,-200579762] 2 42840k4 [0,0,0,-4498203,3672025702] 4 42840k5 [0,0,0,-4443123,3766333678] 2 42840k6 [0,0,0,-71971203,235009953502] 2
42840l (6 curves)	0	2+ 3- 5+ 7+ 17+	2+ 3- 5+ 7+ -4 -2 17+  4
Curve Equation t 42840l1 [0,0,0,-165738,-25959463] 2 42840l2 [0,0,0,-193863,-16548838] 4 42840l3 [0,0,0,656637,-122521138] 2 42840l4 [0,0,0,-1494363,691703462] 4 42840l5 [0,0,0,5037,2016273422] 2 42840l6 [0,0,0,-23801763,44695280702] 2
42840m (6 curves)	0	2+ 3- 5+ 7+ 17+	2+ 3- 5+ 7+ -4 -2 17+ -4
Curve Equation t 42840m1 [0,0,0,-1164378,-494133127] 2 42840m2 [0,0,0,-18742503,-31231242502] 4 42840m3 [0,0,0,-18855003,-30837335002] 4 42840m4 [0,0,0,-299880003,-1998800150002] 2 42840m5 [0,0,0,2753997,-97423307602] 2 42840m6 [0,0,0,-42264003,60958717598] 2
42840n (2 curves)	0	2+ 3- 5+ 7+ 17+	2+ 3- 5+ 7+  6  4 17+  4
Curve Equation t 42840n1 [0,0,0,-12252558,16507764457] 2 42840n2 [0,0,0,-12256383,16496942002] 2
42840o (1 curve)	1	2+ 3- 5+ 7- 17+	2+ 3- 5+ 7-  2 -1 17+  2
Curve Equation t Generators 42840o1 [0,0,0,-75102348,-571386048172] 1 [12442:648270:1]
42840p (2 curves)	1	2+ 3- 5+ 7- 17+	2+ 3- 5+ 7-  2  4 17+ -8
Curve Equation t Generators 42840p1 [0,0,0,-73758,7710113] 2 [136:441:1] 42840p2 [0,0,0,-74703,7502402] 2 [127:252:1]
42840q (2 curves)	1	2+ 3- 5+ 7- 17+	2+ 3- 5+ 7- -2  4 17+  4
Curve Equation t Generators 42840q1 [0,0,0,-2712102798,-54352708820503] 2 [-89017005130321370083330528002744759679660609408:-27150980871863524409537384642319994288800611637:2994977745192806181008788995118860905285801] 42840q2 [0,0,0,-43391254143,-3478975879780942] 2 [4473895584032810891780214936521526601287832140820320649343475609826391932617679545423370336361:-30622902705866683981306571845015173412264566741825074434700604156829428187276344718718579963787500:95489632766664944915437965053010272443195305112502240167519997434926511240799422354579]
42840r (2 curves)	1	2+ 3- 5+ 7- 17+	2+ 3- 5+ 7- -2 -4 17+ -4
Curve Equation t Generators 42840r1 [0,0,0,-318,1937] 2 [-8:63:1] 42840r2 [0,0,0,-1263,-15262] 2 [-17:36:1]
42840s (6 curves)	1	2+ 3- 5+ 7- 17+	2+ 3- 5+ 7-  4 -2 17+  4
Curve Equation t Generators 42840s1 [0,0,0,5622,-5623] 2 [17:308:1] 42840s2 [0,0,0,-22503,-44998] 4 [-121:952:1] 42840s3 [0,0,0,-243003,45951302] 4 [-209:9360:1] 42840s4 [0,0,0,-252003,-48561298] 2 [-281:252:1] 42840s5 [0,0,0,-129603,88975262] 2 [-1294:82251:8] 42840s6 [0,0,0,-3884403,2946690542] 2 [1814:43238:1]
42840t (2 curves)	1	2+ 3- 5+ 7- 17+	2+ 3- 5+ 7- -6  4 17+  0
Curve Equation t Generators 42840t1 [0,0,0,-318,817] 2 [-4:45:1] 42840t2 [0,0,0,-4143,102562] 2 [47:108:1]
42840u (1 curve)	0	2+ 3- 5+ 7- 17-	2+ 3- 5+ 7- -6 -1 17-  5
Curve Equation t 42840u1 [0,0,0,-16803,963198] 1
42840v (4 curves)	1	2+ 3- 5- 7+ 17+	2+ 3- 5- 7+  4 -6 17+  4
Curve Equation t Generators 42840v1 [0,0,0,-9687,-4001366] 2 [435:8608:1] 42840v2 [0,0,0,-441867,-112305674] 4 [-385:864:1] 42840v3 [0,0,0,-741747,59405614] 2 [-682:15750:1] 42840v4 [0,0,0,-7056867,-7215492674] 2 [3090:21964:1]
42840w (4 curves)	0	2+ 3- 5- 7+ 17-	2+ 3- 5- 7+  0  2 17- -4
Curve Equation t 42840w1 [0,0,0,-2442,-45911] 2 42840w2 [0,0,0,-4647,49786] 4 42840w3 [0,0,0,16773,379654] 2 42840w4 [0,0,0,-61347,5844526] 2
42840x (4 curves)	0	2+ 3- 5- 7+ 17-	2+ 3- 5- 7+  0 -2 17-  0
Curve Equation t 42840x1 [0,0,0,-128442,17715049] 4 42840x2 [0,0,0,-141447,13909786] 4 42840x3 [0,0,0,394053,94127686] 2 42840x4 [0,0,0,-885027,-309844946] 2
42840y (4 curves)	0	2+ 3- 5- 7+ 17-	2+ 3- 5- 7+  0 -2 17-  0
Curve Equation t 42840y1 [0,0,0,-850855242,9552820819201] 4 42840y2 [0,0,0,-850868247,9552514195114] 4 42840y3 [0,0,0,-799438827,10757742081046] 2 42840y4 [0,0,0,-902505747,8327662367614] 2
42840z (4 curves)	0	2+ 3- 5- 7+ 17-	2+ 3- 5- 7+  0  6 17-  8
Curve Equation t 42840z1 [0,0,0,-2442,31201] 4 42840z2 [0,0,0,-15447,-715286] 4 42840z3 [0,0,0,5973,-2544554] 2 42840z4 [0,0,0,-244947,-46661186] 2
42840ba (2 curves)	0	2+ 3- 5- 7+ 17-	2+ 3- 5- 7+  6  4 17-  0
Curve Equation t 42840ba1 [0,0,0,-822,-551] 2 42840ba2 [0,0,0,-9327,-345854] 2
42840bb (2 curves)	1	2+ 3- 5- 7- 17-	2+ 3- 5- 7-  2  0 17-  0
Curve Equation t Generators 42840bb1 [0,0,0,-3342,73001] 2 [-8:315:1] 42840bb2 [0,0,0,-7167,-125134] 2 [-25:196:1]
42840bc (1 curve)	1	2+ 3- 5- 7- 17-	2+ 3- 5- 7-  2 -3 17- -6
Curve Equation t Generators 42840bc1 [0,0,0,708,7796] 1 [10:-126:1]
42840bd (4 curves)	1	2+ 3- 5- 7- 17-	2+ 3- 5- 7- -4  6 17-  0
Curve Equation t Generators 42840bd1 [0,0,0,-6807,-3221206] 2 [223:2520:1] 42840bd2 [0,0,0,-371307,-86400106] 4 [1438:48510:1] 42840bd3 [0,0,0,-646707,58956014] 2 [17890:791791:8] 42840bd4 [0,0,0,-5927907,-5555205826] 2 [2950:51282:1]
42840be (4 curves)	1	2+ 3- 5- 7- 17-	2+ 3- 5- 7- -4 -6 17-  0
Curve Equation t Generators 42840be1 [0,0,0,960558,4027555649] 2 [-932:48195:1] 42840be2 [0,0,0,-32865447,69900317786] 4 [4882:-160650:1] 42840be3 [0,0,0,-86394027,-215696067946] 2 [14878:1338750:1] 42840be4 [0,0,0,-520552947,4571353480286] 4 [13207:6300:1]
42840bf (2 curves)	1	2- 3+ 5+ 7+ 17-	2- 3+ 5+ 7+ -6 -2 17- -4
Curve Equation t Generators 42840bf1 [0,0,0,177,-558] 2 [9:-42:1] 42840bf2 [0,0,0,-843,-4842] 2 [-21:60:1]
42840bg (2 curves)	1	2- 3+ 5- 7+ 17+	2- 3+ 5- 7+  2 -2 17+  0
Curve Equation t Generators 42840bg1 [0,0,0,-7647,2168546] 2 [1:1470:1] 42840bg2 [0,0,0,-302427,63659654] 2 [-77:9300:1]
42840bh (2 curves)	0	2- 3+ 5- 7- 17+	2- 3+ 5- 7-  0 -4 17+  8
Curve Equation t 42840bh1 [0,0,0,513,5346] 2 42840bh2 [0,0,0,-3267,52974] 2
42840bi (2 curves)	1	2- 3+ 5- 7- 17-	2- 3+ 5- 7-  4 -4 17- -4
Curve Equation t Generators 42840bi1 [0,0,0,-2322,-6939] 2 [-30:189:1] 42840bi2 [0,0,0,9153,-55134] 2 [55:784:1]
42840bj (4 curves)	1	2- 3- 5+ 7+ 17+	2- 3- 5+ 7+  0  6 17+ -4
Curve Equation t Generators 42840bj1 [0,0,0,-12738,-552683] 2 [-66:23:1] 42840bj2 [0,0,0,-16383,-210782] 4 [-111:490:1] 42840bj3 [0,0,0,62997,-1655498] 2 [51:1300:1] 42840bj4 [0,0,0,-154083,23115598] 2 [251:504:1]
42840bk (2 curves)	1	2- 3- 5+ 7+ 17+	2- 3- 5+ 7+ -2  0 17+  4
Curve Equation t Generators 42840bk1 [0,0,0,-6438,-198763] 2 [-46:7:1] 42840bk2 [0,0,0,-7383,-136582] 2 [-59:306:1]
42840bl (2 curves)	1	2- 3- 5+ 7+ 17+	2- 3- 5+ 7+ -2 -2 17+  0
Curve Equation t Generators 42840bl1 [0,0,0,-3,-6802] 2 [34:180:1] 42840bl2 [0,0,0,-5403,-150442] 2 [106:684:1]
42840bm (2 curves)	1	2- 3- 5+ 7+ 17+	2- 3- 5+ 7+ -2 -6 17+  4
Curve Equation t Generators 42840bm1 [0,0,0,-5703843,8024296142] 2 [59901779:4205548512:68921] 42840bm2 [0,0,0,-104118843,408829225142] 2 [557636096974:2120981102028:91733851]
42840bn (4 curves)	1	2- 3- 5+ 7+ 17+	2- 3- 5+ 7+  4 -2 17+  0
Curve Equation t Generators 42840bn1 [0,0,0,-546978,150816773] 2 [238:5841:1] 42840bn2 [0,0,0,-8675103,9834664898] 4 [973:48114:1] 42840bn3 [0,0,0,-8598603,10016627798] 2 [2531:66836:1] 42840bn4 [0,0,0,-138801603,629418981998] 2 [6923:17336:1]
42840bo (2 curves)	0	2- 3- 5+ 7+ 17-	2- 3- 5+ 7+  0  4 17-  6
Curve Equation t 42840bo1 [0,0,0,-14223,-708622] 2 42840bo2 [0,0,0,-232923,-43267642] 2
42840bp (2 curves)	0	2- 3- 5+ 7+ 17-	2- 3- 5+ 7+  2  2 17-  4
Curve Equation t 42840bp1 [0,0,0,-8643,352942] 2 42840bp2 [0,0,0,-143643,20953942] 2
42840bq (1 curve)	0	2- 3- 5+ 7+ 17-	2- 3- 5+ 7+ -2  1 17- -2
Curve Equation t 42840bq1 [0,0,0,69252,13709572] 1
42840br (4 curves)	0	2- 3- 5+ 7+ 17-	2- 3- 5+ 7+  4 -2 17-  4
Curve Equation t 42840br1 [0,0,0,177,-16238] 2 42840br2 [0,0,0,-8643,-300242] 4 42840br3 [0,0,0,-21243,775798] 2 42840br4 [0,0,0,-137163,-19552538] 2
42840bs (2 curves)	0	2- 3- 5+ 7+ 17-	2- 3- 5+ 7+  6  4 17-  2
Curve Equation t 42840bs1 [0,0,0,-14643,738558] 2 42840bs2 [0,0,0,-239643,45153558] 2
42840bt (2 curves)	0	2- 3- 5+ 7- 17+	2- 3- 5+ 7-  2  0 17+  2
Curve Equation t 42840bt1 [0,0,0,-3936243,-3006795458] 2 42840bt2 [0,0,0,-62985243,-192400558058] 2
42840bu (2 curves)	0	2- 3- 5+ 7- 17+	2- 3- 5+ 7-  2  4 17+ -4
Curve Equation t 42840bu1 [0,0,0,-2256798,-1304894747] 2 42840bu2 [0,0,0,-2352423,-1188289622] 2
42840bv (1 curve)	0	2- 3- 5+ 7- 17+	2- 3- 5+ 7-  2 -5 17+  2
Curve Equation t 42840bv1 [0,0,0,-638508,327059332] 1
42840bw (4 curves)	2	2- 3- 5+ 7- 17+	2- 3- 5+ 7- -4 -6 17+ -4
Curve Equation t Generators 42840bw1 [0,0,0,-1578,11653] 2 [-22:189:1]&[-18:185:1] 42840bw2 [0,0,0,-21423,1206322] 4 [-159:770:1]&[101:-270:1] 42840bw3 [0,0,0,-17643,1645558] 2 [59:-900:1]&[158:1674:1] 42840bw4 [0,0,0,-342723,77225902] 2 [339:32:1]&[534:6818:1]
42840bx (2 curves)	1	2- 3- 5+ 7- 17-	2- 3- 5+ 7-  0  4 17-  2
Curve Equation t Generators 42840bx1 [0,0,0,177,-3278] 2 [29:162:1] 42840bx2 [0,0,0,-2523,-44858] 2 [59:108:1]
42840by (4 curves)	0	2- 3- 5- 7+ 17+	2- 3- 5- 7+  4  6 17+ -8
Curve Equation t 42840by1 [0,0,0,-2275887,1321521266] 4 42840by2 [0,0,0,-2276067,1321301774] 4 42840by3 [0,0,0,-1963947,1696657286] 2 42840by4 [0,0,0,-2591067,931898774] 2
42840bz (2 curves)	0	2- 3- 5- 7+ 17+	2- 3- 5- 7+ -4  4 17+  6
Curve Equation t 42840bz1 [0,0,0,-909327,-466005454] 2 42840bz2 [0,0,0,-16096827,-24854092954] 2
42840ca (1 curve)	1	2- 3- 5- 7+ 17-	2- 3- 5- 7+  2  1 17-  6
Curve Equation t Generators 42840ca1 [0,0,0,-42132,3498644] 1 [28:1530:1]
42840cb (2 curves)	1	2- 3- 5- 7+ 17-	2- 3- 5- 7+  2  4 17-  0
Curve Equation t Generators 42840cb1 [0,0,0,-1435062,-656078659] 2 [1382:425:1] 42840cb2 [0,0,0,-2540487,493784426] 2 [-539:41310:1]
42840cc (1 curve)	1	2- 3- 5- 7+ 17-	2- 3- 5- 7+ -2  1 17-  1
Curve Equation t Generators 42840cc1 [0,0,0,-58827,19431974] 1 [130:34391:8]
42840cd (2 curves)	1	2- 3- 5- 7+ 17-	2- 3- 5- 7+ -2  4 17-  4
Curve Equation t Generators 42840cd1 [0,0,0,-822,-6739] 2 [-14:45:1] 42840cd2 [0,0,0,-4647,116426] 2 [-35:486:1]
42840ce (2 curves)	1	2- 3- 5- 7+ 17-	2- 3- 5- 7+ -2 -4 17-  2
Curve Equation t Generators 42840ce1 [0,0,0,12093,498094] 2 [83:1440:1] 42840ce2 [0,0,0,-68907,4693894] 2 [218:180:1]
42840cf (2 curves)	1	2- 3- 5- 7+ 17-	2- 3- 5- 7+ -2 -4 17- -4
Curve Equation t Generators 42840cf1 [0,0,0,-4234422,3316469389] 2 [2018:-54675:1] 42840cf2 [0,0,0,-7985127,-3452052854] 2 [-1303:68850:1]
42840cg (4 curves)	1	2- 3- 5- 7+ 17-	2- 3- 5- 7+  4  2 17- -4
Curve Equation t Generators 42840cg1 [0,0,0,-24762,-893891] 4 [-127:450:1] 42840cg2 [0,0,0,-349887,-79639166] 4 [1023:25160:1] 42840cg3 [0,0,0,-303987,-101294786] 2 [8130:202279:8] 42840cg4 [0,0,0,-5597787,-5097681146] 2 [4110:203278:1]
42840ch (4 curves)	1	2- 3- 5- 7+ 17-	2- 3- 5- 7+  4  2 17- -4
Curve Equation t Generators 42840ch1 [0,0,0,-373602,71780389] 2 [-570:9977:1] 42840ch2 [0,0,0,-5667807,5193394306] 4 [-2263:80190:1] 42840ch3 [0,0,0,-5359107,5784184366] 2 [32235:-5773064:1] 42840ch4 [0,0,0,-90683787,332385894934] 2 [32723:-5692500:1]
42840ci (4 curves)	1	2- 3- 5- 7+ 17-	2- 3- 5- 7+ -4  2 17-  4
Curve Equation t Generators 42840ci1 [0,0,0,-57522,-5309939] 2 [-138:5:1] 42840ci2 [0,0,0,-59727,-4880846] 4 [-147:850:1] 42840ci3 [0,0,0,97773,-26269346] 2 [483:11560:1] 42840ci4 [0,0,0,-252507,43969606] 2 [587:9900:1]
42840cj (2 curves)	1	2- 3- 5- 7- 17+	2- 3- 5- 7- -4  4 17+  2
Curve Equation t Generators 42840cj1 [0,0,0,12993,171106] 2 [437:9450:1] 42840cj2 [0,0,0,-54507,1399606] 2 [-93:2380:1]
42840ck (2 curves)	1	2- 3- 5- 7- 17+	2- 3- 5- 7- -6 -2 17+ -4
Curve Equation t Generators 42840ck1 [0,0,0,74013,-5259634] 2 [8002:716220:1] 42840ck2 [0,0,0,-363387,-46287754] 2 [97494470:-8702141508:12167]
42840cl (2 curves)	0	2- 3- 5- 7- 17-	2- 3- 5- 7-  2  2 17- -8
Curve Equation t 42840cl1 [0,0,0,-3473624307,-82027086208706] 2 42840cl2 [0,0,0,-56207999307,-5129139195583706] 2
42840cm (4 curves)	0	2- 3- 5- 7- 17-	2- 3- 5- 7- -4  2 17-  4
Curve Equation t 42840cm1 [0,0,0,78,-26651] 2 42840cm2 [0,0,0,-12927,-554654] 4 42840cm3 [0,0,0,-28227,1009006] 2 42840cm4 [0,0,0,-205707,-35910506] 2
42840cn (2 curves)	0	2- 3- 5- 7- 17-	2- 3- 5- 7-  6  4 17- -4
Curve Equation t 42840cn1 [0,0,0,-119622,2039861] 2 42840cn2 [0,0,0,-1225047,-519499654] 2
42840co (2 curves)	2	2- 3- 5- 7- 17-	2- 3- 5- 7- -6 -4 17- -8
Curve Equation t Generators 42840co1 [0,0,0,-9462,-254459] 2 [-78:95:1]&[-58:315:1] 42840co2 [0,0,0,-55767,4866874] 2 [173:-630:1]&[-247:1890:1]

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