Cremona's table of elliptic curves

71760 = 2⁴ · 3 · 5 · 13 · 23

Class	r	Atkin-Lehner	Eigenvalues
71760a (2 curves)	1	2+ 3+ 5+ 13+ 23+	2+ 3+ 5+  4  2 13+ -4  4
Curve Equation t Generators 71760a1 [0,-1,0,-276,-6624] 2 [456:9720:1] 71760a2 [0,-1,0,-7296,-236880] 2 [3674:77175:8]
71760b (2 curves)	0	2+ 3+ 5+ 13+ 23-	2+ 3+ 5+ -2  0 13+ -2 -6
Curve Equation t 71760b1 [0,-1,0,-67731,-6762150] 2 71760b2 [0,-1,0,-68076,-6689424] 2
71760c (4 curves)	1	2+ 3+ 5+ 13- 23-	2+ 3+ 5+  0  4 13- -2  0
Curve Equation t Generators 71760c1 [0,-1,0,409,2706] 2 [516:5145:64] 71760c2 [0,-1,0,-2236,27040] 4 [65:390:1] 71760c3 [0,-1,0,-14656,-658544] 2 [-66:130:1] 71760c4 [0,-1,0,-32136,2227680] 2 [3135:5930:27]
71760d (4 curves)	1	2+ 3+ 5+ 13- 23-	2+ 3+ 5+ -4  4 13-  2  8
Curve Equation t Generators 71760d1 [0,-1,0,-37412031,-87546678750] 2 [118638775941994992609302332182:-403617798556330481562135067931736:10250361787963120888247] 71760d2 [0,-1,0,-61326876,38025389376] 4 [840624153120108:11936263901890625:1349965372608] 71760d3 [0,-1,0,239473104,300563611920] 2 [1133053086381604087307539381092:-7709460421475080322928760498046875:24473881172853597132864] 71760d4 [0,-1,0,-744764376,7811716889376] 4 [55745082:-7298426125:5832]
71760e (2 curves)	0	2+ 3+ 5- 13+ 23+	2+ 3+ 5-  2  0 13+ -6  6
Curve Equation t 71760e1 [0,-1,0,-315,162] 2 71760e2 [0,-1,0,-3420,-75600] 2
71760f (2 curves)	1	2+ 3+ 5- 13+ 23-	2+ 3+ 5- -2  4 13+ -2 -2
Curve Equation t Generators 71760f1 [0,-1,0,-2915,-58650] 2 [-30:30:1] 71760f2 [0,-1,0,-6020,91632] 2 [-56:500:1]
71760g (4 curves)	1	2+ 3+ 5- 13- 23+	2+ 3+ 5- -4  4 13-  2  4
Curve Equation t Generators 71760g1 [0,-1,0,-1495,-21758] 2 [2948:4521:64] 71760g2 [0,-1,0,-1500,-21600] 4 [97:858:1] 71760g3 [0,-1,0,-200,-59040] 2 [2559:23606:27] 71760g4 [0,-1,0,-2880,25872] 4 [4:120:1]
71760h (6 curves)	0	2+ 3+ 5- 13- 23-	2+ 3+ 5-  0  4 13- -6 -4
Curve Equation t 71760h1 [0,-1,0,305,-109250] 2 71760h2 [0,-1,0,-32500,-2195648] 4 71760h3 [0,-1,0,-73000,4413952] 8 71760h4 [0,-1,0,-516880,-142859600] 2 71760h5 [0,-1,0,231200,31426912] 4 71760h6 [0,-1,0,-1025200,399767392] 4
71760i (4 curves)	0	2+ 3+ 5- 13- 23-	2+ 3+ 5-  0 -4 13- -2 -4
Curve Equation t 71760i1 [0,-1,0,-1775,-33750] 2 71760i2 [0,-1,0,-29900,-1980000] 4 71760i3 [0,-1,0,-31400,-1768800] 4 71760i4 [0,-1,0,-478400,-127201200] 2
71760j (2 curves)	0	2+ 3- 5+ 13+ 23+	2+ 3- 5+  2  0 13+  6 -6
Curve Equation t 71760j1 [0,1,0,-77354571,261817709004] 2 71760j2 [0,1,0,-1237645196,16758365699004] 2
71760k (2 curves)	0	2+ 3- 5+ 13+ 23+	2+ 3- 5+  2  6 13+  0  0
Curve Equation t 71760k1 [0,1,0,-985416,-377086716] 2 71760k2 [0,1,0,-15769536,-24108556140] 2
71760l (2 curves)	2	2+ 3- 5+ 13+ 23+	2+ 3- 5+ -2 -4 13+ -2  2
Curve Equation t Generators 71760l1 [0,1,0,-1971,-34020] 2 [-24:6:1]&[72:450:1] 71760l2 [0,1,0,-3596,28380] 2 [-53:270:1]&[-26:324:1]
71760m (2 curves)	1	2+ 3- 5+ 13+ 23-	2+ 3- 5+  2  0 13+  2  6
Curve Equation t Generators 71760m1 [0,1,0,-131,-300] 2 [6414:32669:216] 71760m2 [0,1,0,-1756,-28900] 2 [122:1260:1]
71760n (4 curves)	1	2+ 3- 5+ 13- 23+	2+ 3- 5+  0  4 13- -2  4
Curve Equation t Generators 71760n1 [0,1,0,-631,5744] 2 [362:2145:8] 71760n2 [0,1,0,-1476,-13860] 4 [474:10296:1] 71760n3 [0,1,0,4504,-92796] 2 [22:132:1] 71760n4 [0,1,0,-20976,-1176060] 2 [104334:2177461:216]
71760o (2 curves)	1	2+ 3- 5+ 13- 23+	2+ 3- 5+  2  0 13- -2 -4
Curve Equation t Generators 71760o1 [0,1,0,1984,-190716] 2 [64:450:1] 71760o2 [0,1,0,-40136,-2936940] 2 [-116:414:1]
71760p (4 curves)	1	2+ 3- 5+ 13- 23+	2+ 3- 5+ -4  0 13-  2  0
Curve Equation t Generators 71760p1 [0,1,0,-1151,-14376] 2 [40:72:1] 71760p2 [0,1,0,-3796,72380] 4 [-1:276:1] 71760p3 [0,1,0,7704,435780] 4 [-18:540:1] 71760p4 [0,1,0,-57616,5303684] 2 [155:348:1]
71760q (1 curve)	0	2+ 3- 5+ 13- 23-	2+ 3- 5+  5 -2 13- -5  6
Curve Equation t 71760q1 [0,1,0,872919,1288847619] 1
71760r (4 curves)	1	2+ 3- 5- 13+ 23+	2+ 3- 5-  0  0 13+ -6  4
Curve Equation t Generators 71760r1 [0,1,0,140,20540] 2 [-114:3808:27] 71760r2 [0,1,0,-10440,397188] 4 [78:252:1] 71760r3 [0,1,0,-24240,-888972] 2 [308:4578:1] 71760r4 [0,1,0,-165920,25958100] 4 [-170:7020:1]
71760s (2 curves)	0	2+ 3- 5- 13+ 23-	2+ 3- 5-  0  6 13+  0  0
Curve Equation t 71760s1 [0,1,0,140,-292] 2 71760s2 [0,1,0,-640,-3100] 2
71760t (6 curves)	1	2+ 3- 5- 13- 23-	2+ 3- 5-  0 -4 13-  2  4
Curve Equation t Generators 71760t1 [0,1,0,-4095,-101400] 2 [104:780:1] 71760t2 [0,1,0,-7220,71100] 4 [118:936:1] 71760t3 [0,1,0,27280,581700] 2 [2874:60333:8] 71760t4 [0,1,0,-91720,10650500] 8 [10:3120:1] 71760t5 [0,1,0,-68320,16238420] 4 [314:29523:8] 71760t6 [0,1,0,-1467120,683496180] 4 [20901:94562:27]
71760u (2 curves)	1	2+ 3- 5- 13- 23-	2+ 3- 5- -2 -2 13-  0  8
Curve Equation t Generators 71760u1 [0,1,0,3440,-51100] 2 [40:390:1] 71760u2 [0,1,0,-16840,-464812] 2 [196:1950:1]
71760v (1 curve)	0	2- 3+ 5+ 13+ 23+	2- 3+ 5+ -1  3 13+  6  0
Curve Equation t 71760v1 [0,-1,0,-1056,-12864] 1
71760w (1 curve)	0	2- 3+ 5+ 13+ 23+	2- 3+ 5+ -1  6 13+  3  6
Curve Equation t 71760w1 [0,-1,0,1019,48301] 1
71760x (2 curves)	0	2- 3+ 5+ 13+ 23+	2- 3+ 5+  4 -2 13+ -4  0
Curve Equation t 71760x1 [0,-1,0,-1263296,698642496] 2 71760x2 [0,-1,0,-21733616,39002705280] 2
71760y (2 curves)	0	2- 3+ 5+ 13+ 23+	2- 3+ 5+ -4  0 13+  2 -6
Curve Equation t 71760y1 [0,-1,0,-1581,21456] 2 71760y2 [0,-1,0,2644,112716] 2
71760z (2 curves)	1	2- 3+ 5+ 13+ 23-	2- 3+ 5+  2  4 13+  2 -4
Curve Equation t Generators 71760z1 [0,-1,0,-1841,-29784] 2 [11274:422877:8] 71760z2 [0,-1,0,-1516,-40964] 2 [104405154:-3916387817:74088]
71760ba (4 curves)	1	2- 3+ 5+ 13- 23+	2- 3+ 5+ -2  0 13-  6  4
Curve Equation t Generators 71760ba1 [0,-1,0,-292237816,-1979227523984] 2 [1171980806011528348836:413040854143996562060800:9254518812512351] 71760ba2 [0,-1,0,-4713826936,-124566901558160] 2 [278628606739197490399763428539497445750279:85030964932518041565521088517033551321042500:2065197598910102622092279971359348703] 71760ba3 [0,-1,0,1385803544,-6908062355600] 2 [2779624429596:785068544000000:241804367] 71760ba4 [0,-1,0,-5903315176,-56905585479824] 2 [4470492030811780869:-2029491721295898437500:19225139807069]
71760bb (1 curve)	0	2- 3+ 5+ 13- 23-	2- 3+ 5+ -1  3 13-  6  4
Curve Equation t 71760bb1 [0,-1,0,344,-2000] 1
71760bc (4 curves)	0	2- 3+ 5+ 13- 23-	2- 3+ 5+  4  6 13- -6  4
Curve Equation t 71760bc1 [0,-1,0,-18101,-930924] 2 71760bc2 [0,-1,0,-14996,-1263780] 2 71760bc3 [0,-1,0,-55541,3937680] 2 71760bc4 [0,-1,0,126964,24232236] 2
71760bd (2 curves)	1	2- 3+ 5- 13+ 23+	2- 3+ 5- -2  4 13+  6  4
Curve Equation t Generators 71760bd1 [0,-1,0,-1019585,-36657108] 2 [-216:13170:1] 71760bd2 [0,-1,0,4058540,-296657108] 2 [1172094:-92016595:216]
71760be (1 curve)	1	2- 3+ 5- 13+ 23+	2- 3+ 5-  3 -1 13+ -4 -6
Curve Equation t Generators 71760be1 [0,-1,0,140,-260] 1 [345:1478:125]
71760bf (2 curves)	1	2- 3+ 5- 13+ 23+	2- 3+ 5-  4 -2 13+  0  4
Curve Equation t Generators 71760bf1 [0,-1,0,-640,13312] 2 [-6:130:1] 71760bf2 [0,-1,0,-13120,582400] 2 [42:322:1]
71760bg (2 curves)	0	2- 3+ 5- 13+ 23-	2- 3+ 5-  0 -4 13+  4  0
Curve Equation t 71760bg1 [0,-1,0,-125,2352] 2 71760bg2 [0,-1,0,-3500,80652] 2
71760bh (1 curve)	0	2- 3+ 5- 13+ 23-	2- 3+ 5-  1  5 13+  6 -8
Curve Equation t 71760bh1 [0,-1,0,-53360,90466752] 1
71760bi (1 curve)	0	2- 3+ 5- 13+ 23-	2- 3+ 5-  3 -3 13+ -2  4
Curve Equation t 71760bi1 [0,-1,0,-58280,-5424528] 1
71760bj (2 curves)	0	2- 3+ 5- 13+ 23-	2- 3+ 5-  4 -4 13+  0  4
Curve Equation t 71760bj1 [0,-1,0,75,0] 2 71760bj2 [0,-1,0,-300,300] 2
71760bk (2 curves)	0	2- 3+ 5- 13- 23+	2- 3+ 5-  2  4 13-  6  8
Curve Equation t 71760bk1 [0,-1,0,-6440,-800400] 2 71760bk2 [0,-1,0,-174920,-28026768] 2
71760bl (2 curves)	1	2- 3+ 5- 13- 23-	2- 3+ 5-  1  3 13-  0 -2
Curve Equation t Generators 71760bl1 [0,-1,0,-2340,106812] 1 [29:250:1] 71760bl2 [0,-1,0,-257340,50332812] 1 [389:2990:1]
71760bm (1 curve)	1	2- 3- 5+ 13+ 23+	2- 3- 5+ -1  3 13+  8  2
Curve Equation t Generators 71760bm1 [0,1,0,-454156,-118429000] 1 [2731:137904:1]
71760bn (2 curves)	1	2- 3- 5+ 13+ 23+	2- 3- 5+ -2  2 13+ -4  0
Curve Equation t Generators 71760bn1 [0,1,0,-3013616,2243665620] 2 [1012:-15210:1] 71760bn2 [0,1,0,-49738736,134999076564] 2 [-8108:73002:1]
71760bo (4 curves)	0	2- 3- 5+ 13+ 23-	2- 3- 5+  0  4 13+  2 -8
Curve Equation t 71760bo1 [0,1,0,-4378336,3524761460] 2 71760bo2 [0,1,0,-4460256,3385923444] 4 71760bo3 [0,1,0,4179744,14932419444] 2 71760bo4 [0,1,0,-14410976,-17044894860] 2
71760bp (1 curve)	0	2- 3- 5+ 13+ 23-	2- 3- 5+  1  5 13+  2 -4
Curve Equation t 71760bp1 [0,1,0,824,-118156] 1
71760bq (2 curves)	0	2- 3- 5+ 13+ 23-	2- 3- 5+  4  6 13+ -8  8
Curve Equation t 71760bq1 [0,1,0,-53056,-4778956] 2 71760bq2 [0,1,0,-851776,-302861260] 2
71760br (2 curves)	2	2- 3- 5+ 13+ 23-	2- 3- 5+ -4 -2 13+  0  0
Curve Equation t Generators 71760br1 [0,1,0,-16656,854100] 2 [906:-5265:8]&[-124:1014:1] 71760br2 [0,1,0,-269376,53723124] 2 [-276:10350:1]&[207:2622:1]
71760bs (1 curve)	0	2- 3- 5+ 13+ 23-	2- 3- 5+ -5  5 13+  2  0
Curve Equation t 71760bs1 [0,1,0,-180896,-31196940] 1
71760bt (4 curves)	1	2- 3- 5+ 13- 23-	2- 3- 5+  4  0 13-  2  0
Curve Equation t Generators 71760bt1 [0,1,0,28704,2347380] 2 [47:1950:1] 71760bt2 [0,1,0,-187616,23373684] 4 [90:2688:1] 71760bt3 [0,1,0,-1048736,-394441740] 2 [-4662:35007:8] 71760bt4 [0,1,0,-2787616,1790333684] 4 [442:25392:1]
71760bu (4 curves)	1	2- 3- 5+ 13- 23-	2- 3- 5+ -4 -4 13- -6 -8
Curve Equation t Generators 71760bu1 [0,1,0,-46456,-5881900] 2 [640236:-9128125:1728] 71760bu2 [0,1,0,-846456,-299961900] 4 [6950:574080:1] 71760bu3 [0,1,0,-950456,-221712300] 4 [-788:6210:1] 71760bu4 [0,1,0,-13542456,-19186531500] 2 [59050:4256265:8]
71760bv (1 curve)	1	2- 3- 5+ 13- 23-	2- 3- 5+ -5  3 13- -4  6
Curve Equation t Generators 71760bv1 [0,1,0,-156,-936] 1 [15:18:1]
71760bw (2 curves)	0	2- 3- 5- 13+ 23+	2- 3- 5-  2  6 13+ -4 -4
Curve Equation t 71760bw1 [0,1,0,-794160,417186900] 2 71760bw2 [0,1,0,-14503440,21249808788] 2
71760bx (1 curve)	0	2- 3- 5- 13+ 23+	2- 3- 5- -3 -5 13+  2  8
Curve Equation t 71760bx1 [0,1,0,39920,-7056172] 1
71760by (2 curves)	1	2- 3- 5- 13+ 23-	2- 3- 5-  0 -2 13+ -4  4
Curve Equation t Generators 71760by1 [0,1,0,89840,-179692] 2 [236:-5850:1] 71760by2 [0,1,0,-359440,-1797100] 2 [-580:3450:1]
71760bz (2 curves)	1	2- 3- 5- 13+ 23-	2- 3- 5-  0 -2 13+ -4 -4
Curve Equation t Generators 71760bz1 [0,1,0,66240,-9045900] 2 [138:1656:1] 71760bz2 [0,1,0,-461040,-93621612] 2 [4532:301530:1]
71760ca (2 curves)	1	2- 3- 5- 13+ 23-	2- 3- 5-  2 -4 13+  6  0
Curve Equation t Generators 71760ca1 [0,1,0,-185,858] 2 [-14:30:1] 71760ca2 [0,1,0,140,3848] 2 [263:4278:1]
71760cb (2 curves)	1	2- 3- 5- 13- 23+	2- 3- 5-  0 -2 13-  2  8
Curve Equation t Generators 71760cb1 [0,1,0,-85,158] 2 [-2:18:1] 71760cb2 [0,1,0,260,1400] 2 [122:765:8]
71760cc (6 curves)	1	2- 3- 5- 13- 23+	2- 3- 5-  0  4 13-  2 -4
Curve Equation t Generators 71760cc1 [0,1,0,8333520,18705548628] 2 [171:141900:1] 71760cc2 [0,1,0,-75552560,215703618900] 4 [-4580:682410:1] 71760cc3 [0,1,0,-334337840,-2144521648812] 2 [33196:4831050:1] 71760cc4 [0,1,0,-1158944560,15185147561300] 8 [36380:4601430:1] 71760cc5 [0,1,0,-1109190960,16548336496980] 4 [2466548028:328302850086:68921] 71760cc6 [0,1,0,-18542970160,971883705211220] 4 [2007575692:44117527086:24389]
71760cd (4 curves)	0	2- 3- 5- 13- 23-	2- 3- 5-  0  0 13-  2 -4
Curve Equation t 71760cd1 [0,1,0,-8840,-300300] 2 71760cd2 [0,1,0,-29320,1575668] 4 71760cd3 [0,1,0,59000,9312500] 2 71760cd4 [0,1,0,-445320,114228468] 4
71760ce (1 curve)	0	2- 3- 5- 13- 23-	2- 3- 5-  1  3 13- -6  4
Curve Equation t 71760ce1 [0,1,0,234760,-8474412] 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