Cremona's table of elliptic curves

49686 = 2 · 3 · 7² · 13²

Class	r	Atkin-Lehner	Eigenvalues
49686a (2 curves)	1	2+ 3+ 7+ 13+	2+ 3+  0 7+  2 13+  4 -1
Curve Equation t Generators 49686a1 [1,1,0,465,-5403] 1 [14:57:1] 49686a2 [1,1,0,-470915,-124579671] 1 [1288:36875:1]
49686b (1 curve)	1	2+ 3+ 7+ 13+	2+ 3+  0 7+  5 13+  7 -7
Curve Equation t Generators 49686b1 [1,1,0,-646090,-357839516] 1 [1240:26758:1]
49686c (2 curves)	1	2+ 3+ 7+ 13+	2+ 3+ -1 7+ -5 13+ -4 -8
Curve Equation t Generators 49686c1 [1,1,0,-8453,686379] 1 [265:4008:1] 49686c2 [1,1,0,-1167793,-504438059] 1 [9183:869054:1]
49686d (2 curves)	0	2+ 3+ 7- 13+	2+ 3+  0 7-  2 13+ -3  6
Curve Equation t 49686d1 [1,1,0,10,-762] 1 49686d2 [1,1,0,-21830,1234836] 1
49686e (2 curves)	0	2+ 3+ 7- 13+	2+ 3+  0 7- -3 13+  3 -5
Curve Equation t 49686e1 [1,1,0,-10955935,-13821478523] 1 49686e2 [1,1,0,-83621710,286866591796] 1
49686f (2 curves)	0	2+ 3+ 7- 13+	2+ 3+  0 7- -3 13+ -3  5
Curve Equation t 49686f1 [1,1,0,-728900,24312072] 1 49686f2 [1,1,0,-42713570,107429494866] 1
49686g (2 curves)	0	2+ 3+ 7- 13+	2+ 3+  0 7- -5 13+ -3 -1
Curve Equation t 49686g1 [1,1,0,-1728535,-875159501] 1 49686g2 [1,1,0,-133680355,594847722253] 1
49686h (1 curve)	0	2+ 3+ 7- 13+	2+ 3+ -1 7-  1 13+  6 -4
Curve Equation t 49686h1 [1,1,0,-239138,-620086956] 1
49686i (2 curves)	0	2+ 3+ 7- 13+	2+ 3+ -1 7- -5 13+  3 -1
Curve Equation t 49686i1 [1,1,0,5912462,62524364596] 1 49686i2 [1,1,0,-30428501548,2042990125308826] 1
49686j (1 curve)	0	2+ 3+ 7- 13+	2+ 3+  2 7-  3 13+  7  5
Curve Equation t 49686j1 [1,1,0,-223759,-40569563] 1
49686k (4 curves)	0	2+ 3+ 7- 13+	2+ 3+  2 7-  4 13+ -6 -4
Curve Equation t 49686k1 [1,1,0,-58139,4810317] 2 49686k2 [1,1,0,-223759,-35700335] 4 49686k3 [1,1,0,355911,-189312885] 2 49686k4 [1,1,0,-3453349,-2471457113] 2
49686l (1 curve)	0	2+ 3+ 7- 13+	2+ 3+  2 7- -4 13+ -7 -2
Curve Equation t 49686l1 [1,1,0,-10202364,12546724338] 1
49686m (2 curves)	0	2+ 3+ 7- 13+	2+ 3+ -2 7- -4 13+  2  4
Curve Equation t 49686m1 [1,1,0,-6303196,6088379536] 2 49686m2 [1,1,0,-6255876,6184353960] 2
49686n (1 curve)	0	2+ 3+ 7- 13+	2+ 3+  3 7-  1 13+ -3 -1
Curve Equation t 49686n1 [1,1,0,49514,-4124882] 1
49686o (2 curves)	0	2+ 3+ 7- 13+	2+ 3+  3 7- -3 13+ -6 -4
Curve Equation t 49686o1 [1,1,0,-3721,-167747] 1 49686o2 [1,1,0,31769,3345763] 1
49686p (1 curve)	0	2+ 3+ 7- 13+	2+ 3+ -3 7-  5 13+ -3  3
Curve Equation t 49686p1 [1,1,0,-1921364,-1992740784] 1
49686q (2 curves)	0	2+ 3+ 7- 13+	2+ 3+ -3 7-  6 13+  3 -2
Curve Equation t 49686q1 [1,1,0,-513594,-248265324] 1 49686q2 [1,1,0,4330791,4639719141] 1
49686r (1 curve)	0	2+ 3+ 7- 13+	2+ 3+  4 7- -1 13+  5 -5
Curve Equation t 49686r1 [1,1,0,-263,-1035] 1
49686s (1 curve)	0	2+ 3+ 7- 13+	2+ 3+ -4 7-  1 13+ -3 -1
Curve Equation t 49686s1 [1,1,0,-30846897,-67586632875] 1
49686t (1 curve)	0	2+ 3+ 7- 13+	2+ 3+ -4 7- -2 13+ -7  2
Curve Equation t 49686t1 [1,1,0,-307752,-65860920] 1
49686u (1 curve)	1	2+ 3+ 7- 13-	2+ 3+ -1 7-  3 13-  7  3
Curve Equation t Generators 49686u1 [1,1,0,-384081233,-3135674078571] 1 [43486679981811711975:40093087497596588507979:51077199691727]
49686v (4 curves)	1	2+ 3+ 7- 13-	2+ 3+  2 7-  0 13- -2  4
Curve Equation t Generators 49686v1 [1,1,0,-3743184,2782381932] 2 [-316:62878:1] 49686v2 [1,1,0,-2666654,4417200390] 2 [-162210:69690897:1000] 49686v3 [1,1,0,-111934449,-455703455787] 2 [-2677341597222520822:-4250085583046298629:438924018051973] 49686v4 [1,1,0,-94709969,-600709463115] 2 [1555016338658555331347478758934090:-273507442043044445165593649354567013:45657726521547744813906971000]
49686w (4 curves)	1	2+ 3+ 7- 13-	2+ 3+  2 7-  0 13- -2 -6
Curve Equation t Generators 49686w1 [1,1,0,2376,19440] 2 [28:316:1] 49686w2 [1,1,0,-10364,149388] 2 [-46:752:1] 49686w3 [1,1,0,-217389,-39127395] 2 [1429456401254:-15750468209587:2422300607] 49686w4 [1,1,0,-3478829,-2498905443] 2 [-531143386:265324445:493039]
49686x (2 curves)	1	2+ 3+ 7- 13-	2+ 3+ -3 7- -5 13-  3 -1
Curve Equation t Generators 49686x1 [1,1,0,-577294,168587476] 1 [447:95:1] 49686x2 [1,1,0,1190381,873637549] 1 [993:54604:1]
49686y (1 curve)	0	2+ 3- 7+ 13+	2+ 3-  1 7+  1 13+ -6  4
Curve Equation t 49686y1 [1,0,1,-11717788,212654672570] 1
49686z (2 curves)	0	2+ 3- 7+ 13+	2+ 3- -3 7+ -3 13+  6  4
Curve Equation t 49686z1 [1,0,1,-182355,56990182] 1 49686z2 [1,0,1,1556655,-1142926718] 1
49686ba (1 curve)	0	2+ 3- 7+ 13+	2+ 3-  4 7+  1 13+  3  1
Curve Equation t 49686ba1 [1,0,1,-629529,196955644] 1
49686bb (2 curves)	1	2+ 3- 7- 13+	2+ 3-  0 7-  2 13+  3 -6
Curve Equation t Generators 49686bb1 [1,0,1,-446,-3664] 1 [1326:7580:27] 49686bb2 [1,0,1,464,262784] 1 [4:-517:1]
49686bc (2 curves)	1	2+ 3- 7- 13+	2+ 3-  0 7-  2 13+ -4  1
Curve Equation t Generators 49686bc1 [1,0,1,22759,1921532] 1 [456365:16533054:343] 49686bc2 [1,0,1,-23074861,42661602596] 1 [2773:-1414:1]
49686bd (1 curve)	1	2+ 3- 7- 13+	2+ 3-  0 7-  5 13+ -7  7
Curve Equation t Generators 49686bd1 [1,0,1,-13186,1041380] 1 [1:1013:1]
49686be (2 curves)	1	2+ 3- 7- 13+	2+ 3-  0 7- -5 13+  3  1
Curve Equation t Generators 49686be1 [1,0,1,-2728171,-1734639658] 1 [-80138793787440:42555822833749:83855130633] 49686be2 [1,0,1,-84698241,299925614146] 1 [5198:8205:1]
49686bf (1 curve)	1	2+ 3- 7- 13+	2+ 3-  1 7-  2 13+ -5  2
Curve Equation t Generators 49686bf1 [1,0,1,-173,33464] 1 [39:274:1]
49686bg (2 curves)	1	2+ 3- 7- 13+	2+ 3-  1 7- -5 13+  4  8
Curve Equation t Generators 49686bg1 [1,0,1,-173,-2026] 1 [5894:1191:343] 49686bg2 [1,0,1,-23833,1467260] 1 [40:740:1]
49686bh (1 curve)	1	2+ 3- 7- 13+	2+ 3-  2 7-  0 13+ -1 -6
Curve Equation t Generators 49686bh1 [1,0,1,-58140,-7502246] 1 [326:2703:1]
49686bi (2 curves)	1	2+ 3- 7- 13+	2+ 3-  2 7- -4 13+ -2 -4
Curve Equation t Generators 49686bi1 [1,0,1,-308856630,-2089240750712] 2 [-1267895:485841:125] 49686bi2 [1,0,1,-306537950,-2122153022104] 2 [12666480:-3973597909:125]
49686bj (1 curve)	1	2+ 3- 7- 13+	2+ 3- -2 7- -1 13+  1 -1
Curve Equation t Generators 49686bj1 [1,0,1,-405942,-50977496] 1 [-11526:185996:27]
49686bk (6 curves)	1	2+ 3- 7- 13+	2+ 3- -2 7-  4 13+ -2 -4
Curve Equation t Generators 49686bk1 [1,0,1,-33297,-5167004] 2 [39055:-502974:125] 49686bk2 [1,0,1,-695777,-223255420] 4 [-489:574:1] 49686bk3 [1,0,1,-861397,-108977620] 4 [-815:7610:1] 49686bk4 [1,0,1,-11129837,-14292541924] 2 [-2563770:1276742:1331] 49686bk5 [1,0,1,3196293,-840984896] 2 [368:19440:1] 49686bk6 [1,0,1,-7569007,7937471336] 2 [1756:6980:1]
49686bl (1 curve)	1	2+ 3- 7- 13+	2+ 3-  3 7- -1 13+ -7  1
Curve Equation t Generators 49686bl1 [1,0,1,-832108177,9291628742372] 1 [6150:2096158:1]
49686bm (1 curve)	1	2+ 3- 7- 13+	2+ 3-  3 7- -4 13+  5  4
Curve Equation t Generators 49686bm1 [1,0,1,-4632,-225158] 1 [95:393:1]
49686bn (1 curve)	1	2+ 3- 7- 13+	2+ 3-  3 7-  5 13+  3 -3
Curve Equation t Generators 49686bn1 [1,0,1,-39212,5804138] 1 [144:1702:1]
49686bo (1 curve)	1	2+ 3- 7- 13+	2+ 3- -3 7-  1 13+  3  1
Curve Equation t Generators 49686bo1 [1,0,1,1010,12170] 1 [144:1702:1]
49686bp (1 curve)	1	2+ 3- 7- 13+	2+ 3-  4 7- -2 13+  7 -2
Curve Equation t Generators 49686bp1 [1,0,1,-15079874,22545055964] 1 [3042:67936:1]
49686bq (1 curve)	1	2+ 3- 7- 13+	2+ 3- -4 7- -1 13+ -5  5
Curve Equation t Generators 49686bq1 [1,0,1,-12913,316292] 1 [4:512:1]
49686br (1 curve)	1	2+ 3- 7- 13+	2+ 3- -4 7- -3 13+  5 -3
Curve Equation t Generators 49686br1 [1,0,1,-6003898,-3966747718] 1 [-1676:38102:1]
49686bs (1 curve)	0	2+ 3- 7- 13-	2+ 3- -1 7- -1 13-  1  1
Curve Equation t 49686bs1 [1,0,1,778241,-5978542] 1
49686bt (2 curves)	0	2- 3+ 7+ 13+	2- 3+  0 7+ -2 13+  4  1
Curve Equation t 49686bt1 [1,1,1,78497,-12263035] 1 49686bt2 [1,1,1,-79584723,-273303613731] 1
49686bu (1 curve)	0	2- 3+ 7+ 13+	2- 3+ -1 7+  3 13+ -2  0
Curve Equation t 49686bu1 [1,1,1,4483989,1942218585] 1
49686bv (1 curve)	0	2- 3+ 7+ 13+	2- 3+  2 7+ -3 13+  1  3
Curve Equation t 49686bv1 [1,1,1,3968,59093] 1
49686bw (2 curves)	1	2- 3+ 7- 13+	2- 3+  0 7- -2 13+ -3 -6
Curve Equation t Generators 49686bw1 [1,1,1,1602,-1682283] 1 [1156504084:69575123541:314432] 49686bw2 [1,1,1,-3689358,2731381323] 1 [1049:3591:1]
49686bx (2 curves)	1	2- 3+ 7- 13+	2- 3+  0 7-  3 13+  3  5
Curve Equation t Generators 49686bx1 [1,1,1,-64828,-6316003] 1 [-155:273:1] 49686bx2 [1,1,1,-494803,130381649] 1 [307:2590:1]
49686by (2 curves)	1	2- 3+ 7- 13+	2- 3+  0 7-  3 13+ -3 -5
Curve Equation t Generators 49686by1 [1,1,1,-4313,9407] 1 [-43:364:1] 49686by2 [1,1,1,-252743,48801059] 1 [11444:190099:64]
49686bz (2 curves)	1	2- 3+ 7- 13+	2- 3+  0 7-  5 13+ -3  1
Curve Equation t Generators 49686bz1 [1,1,1,-10228,-402277] 1 [-3788:2499:64] 49686bz2 [1,1,1,-791008,270450305] 1 [265:8785:1]
49686ca (1 curve)	1	2- 3+ 7- 13+	2- 3+  1 7- -1 13+  5  1
Curve Equation t Generators 49686ca1 [1,1,1,56020,-16748971] 1 [35855:581791:125]
49686cb (1 curve)	1	2- 3+ 7- 13+	2- 3+  1 7- -3 13+ -5  1
Curve Equation t Generators 49686cb1 [1,1,1,-62280,6849513] 1 [447:8057:1]
49686cc (1 curve)	1	2- 3+ 7- 13+	2- 3+ -1 7- -5 13+ -3  5
Curve Equation t Generators 49686cc1 [1,1,1,-25658851,50020048385] 1 [4087:113890:1]
49686cd (2 curves)	1	2- 3+ 7- 13+	2- 3+  2 7-  4 13+ -6 -4
Curve Equation t Generators 49686cd1 [1,1,1,-9927317,-2767486597] 2 [-2881:45380:1] 49686cd2 [1,1,1,38528363,-21781495429] 2 [105795:-13419508:125]
49686ce (1 curve)	1	2- 3+ 7- 13+	2- 3+ -2 7- -3 13+ -5  1
Curve Equation t Generators 49686ce1 [1,1,1,-343834,-88999513] 1 [3125:169803:1]
49686cf (1 curve)	1	2- 3+ 7- 13+	2- 3+ -2 7- -3 13+  7 -5
Curve Equation t Generators 49686cf1 [1,1,1,-37815359,-88942253275] 1 [-3781:3458:1]
49686cg (4 curves)	1	2- 3+ 7- 13+	2- 3+ -2 7-  4 13+  2 -4
Curve Equation t Generators 49686cg1 [1,1,1,-468049,119653295] 4 [-203:14466:1] 49686cg2 [1,1,1,-1130529,-295589169] 4 [9085439:736647520:1331] 49686cg3 [1,1,1,3341211,-2050299945] 2 [166987617:-8631744394:132651] 49686cg4 [1,1,1,-16201949,-25103146489] 2 [48124804365:3273683831446:6539203]
49686ch (1 curve)	1	2- 3+ 7- 13+	2- 3+ -2 7-  4 13+ -7  2
Curve Equation t Generators 49686ch1 [1,1,1,-60369,5687625] 1 [8756:2793:64]
49686ci (2 curves)	1	2- 3+ 7- 13+	2- 3+  3 7- -3 13+  0 -4
Curve Equation t Generators 49686ci1 [1,1,1,194431,40553183] 1 [4763:327844:1] 49686ci2 [1,1,1,-5892104,5530607753] 1 [1253:-11443:1]
49686cj (3 curves)	1	2- 3+ 7- 13+	2- 3+  3 7- -3 13+  3 -7
Curve Equation t Generators 49686cj1 [1,1,1,111621,-136444911] 1 [8637:798938:1] 49686cj2 [1,1,1,-1006314,3720430839] 1 [447:-58191:1] 49686cj3 [1,1,1,-215774049,1219893596319] 1 [447:1059744:1]
49686ck (2 curves)	1	2- 3+ 7- 13+	2- 3+  3 7- -6 13+  3  2
Curve Equation t Generators 49686ck1 [1,1,1,-3039,-114171] 1 [307:5138:1] 49686ck2 [1,1,1,25626,2121699] 1 [97:-2401:1]
49686cl (1 curve)	1	2- 3+ 7- 13+	2- 3+  4 7-  2 13+ -7 -2
Curve Equation t Generators 49686cl1 [1,1,1,-52010176,-144436390519] 1 [19829218279700317395553811477750868231675:316672445894083073841297171586847451234601:2346915934938234669226688264271435693]
49686cm (1 curve)	1	2- 3+ 7- 13+	2- 3+ -4 7-  1 13+  5  5
Curve Equation t Generators 49686cm1 [1,1,1,-44535,-2051379] 1 [-99:-1134:1]
49686cn (2 curves)	1	2- 3+ 7- 13+	2- 3+ -4 7-  4 13+  0 -4
Curve Equation t Generators 49686cn1 [1,1,1,20530,-24137989] 2 [8715:809377:1] 49686cn2 [1,1,1,-1138810,-455412469] 2 [1092805:100840101:125]
49686co (1 curve)	0	2- 3+ 7- 13-	2- 3+  1 7- -3 13-  7 -3
Curve Equation t 49686co1 [1,1,1,-2272670,-1428126757] 1
49686cp (4 curves)	0	2- 3+ 7- 13-	2- 3+ -2 7-  0 13- -2 -4
Curve Equation t 49686cp1 [1,1,1,-22149,1257927] 2 49686cp2 [1,1,1,-15779,2004491] 2 49686cp3 [1,1,1,-662334,-207675525] 2 49686cp4 [1,1,1,-560414,-273638149] 2
49686cq (4 curves)	0	2- 3+ 7- 13-	2- 3+ -2 7-  0 13- -2  6
Curve Equation t 49686cq1 [1,1,1,401456,40702241] 2 49686cq2 [1,1,1,-1751604,336963297] 2 49686cq3 [1,1,1,-36738829,-85779192829] 2 49686cq4 [1,1,1,-587922189,-5487155647485] 2
49686cr (2 curves)	0	2- 3+ 7- 13-	2- 3+  3 7-  5 13-  3  1
Curve Equation t 49686cr1 [1,1,1,-97562774,370874498483] 1 49686cr2 [1,1,1,201174301,1918375823489] 1
49686cs (1 curve)	1	2- 3- 7+ 13+	2- 3-  2 7+ -3 13+  5 -1
Curve Equation t Generators 49686cs1 [1,0,0,-16847867,30476289297] 1 [3238:97753:1]
49686ct (2 curves)	1	2- 3- 7+ 13+	2- 3- -3 7+ -3 13+  0  4
Curve Equation t Generators 49686ct1 [1,0,0,3968,-117664] 1 [92:-1060:1] 49686ct2 [1,0,0,-120247,-16141399] 1 [1366:47989:1]
49686cu (2 curves)	0	2- 3- 7- 13+	2- 3-  0 7- -2 13+  3  6
Curve Equation t 49686cu1 [1,0,0,-75293,-7973967] 1 49686cu2 [1,0,0,78497,577258499] 1
49686cv (2 curves)	0	2- 3- 7- 13+	2- 3-  0 7- -2 13+ -4 -1
Curve Equation t 49686cv1 [1,0,0,3846352,4217760000] 1 49686cv2 [1,0,0,-3899651428,93731440555388] 1
49686cw (2 curves)	0	2- 3- 7- 13+	2- 3-  0 7-  5 13+  3 -1
Curve Equation t 49686cw1 [1,0,0,-16143,-790791] 1 49686cw2 [1,0,0,-501173,136477431] 1
49686cx (1 curve)	0	2- 3- 7- 13+	2- 3-  1 7-  3 13+  2  0
Curve Equation t 49686cx1 [1,0,0,91510,-5649372] 1
49686cy (1 curve)	0	2- 3- 7- 13+	2- 3-  1 7- -5 13+  3 -5
Curve Equation t 49686cy1 [1,0,0,-523650,-145905852] 1
49686cz (1 curve)	0	2- 3- 7- 13+	2- 3- -1 7-  1 13+  1  7
Curve Equation t 49686cz1 [1,0,0,-898661,332140899] 1
49686da (1 curve)	0	2- 3- 7- 13+	2- 3- -1 7- -1 13+ -5 -1
Curve Equation t 49686da1 [1,0,0,2744979,5753131929] 1
49686db (1 curve)	0	2- 3- 7- 13+	2- 3- -1 7- -2 13+ -5 -2
Curve Equation t 49686db1 [1,0,0,-29156,73550112] 1
49686dc (1 curve)	0	2- 3- 7- 13+	2- 3-  2 7-  1 13+  1  1
Curve Equation t 49686dc1 [1,0,0,-2402,-23388] 1
49686dd (4 curves)	0	2- 3- 7- 13+	2- 3-  2 7-  4 13+ -2 -8
Curve Equation t 49686dd1 [1,0,0,-161652,-522284400] 2 49686dd2 [1,0,0,-10761332,-13464493680] 4 49686dd3 [1,0,0,-19373572,11130341312] 2 49686dd4 [1,0,0,-171743972,-866318323872] 2
49686de (1 curve)	0	2- 3- 7- 13+	2- 3- -2 7-  0 13+ -1  6
Curve Equation t 49686de1 [1,0,0,-9825579,-16472608335] 1
49686df (1 curve)	0	2- 3- 7- 13+	2- 3- -2 7- -3 13+ -1 -3
Curve Equation t 49686df1 [1,0,0,194431,-19685667] 1
49686dg (2 curves)	0	2- 3- 7- 13+	2- 3- -2 7-  4 13+  6  4
Curve Equation t 49686dg1 [1,0,0,-486438534,947788587108] 2 49686dg2 [1,0,0,1887889786,7476716601444] 2
49686dh (1 curve)	0	2- 3- 7- 13+	2- 3- -3 7-  4 13+  5 -4
Curve Equation t 49686dh1 [1,0,0,-782727,-493888851] 1
49686di (1 curve)	0	2- 3- 7- 13+	2- 3-  4 7-  1 13+ -5 -5
Curve Equation t 49686di1 [1,0,0,-2182216,697076288] 1
49686dj (1 curve)	0	2- 3- 7- 13+	2- 3-  4 7-  3 13+  5  3
Curve Equation t 49686dj1 [1,0,0,-35526,-1808262] 1
49686dk (2 curves)	0	2- 3- 7- 13+	2- 3-  4 7-  4 13+  0  4
Curve Equation t 49686dk1 [1,0,0,419,70433] 2 49686dk2 [1,0,0,-23241,1324413] 2
49686dl (1 curve)	0	2- 3- 7- 13+	2- 3- -4 7-  2 13+  7  2
Curve Equation t 49686dl1 [1,0,0,-2548498625,49534036452081] 1
49686dm (1 curve)	1	2- 3- 7- 13-	2- 3-  1 7-  1 13-  1 -1
Curve Equation t Generators 49686dm1 [1,0,0,4605,-2367] 1 [144:1839:1]

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