Cremona's table of elliptic curves

31850 = 2 · 5² · 7² · 13

Class	r	Atkin-Lehner	Eigenvalues
31850a (1 curve)	1	2+ 5+ 7+ 13+	2+  0 5+ 7+  6 13+ -1  0
Curve Equation t Generators 31850a1 [1,-1,0,-66992,720166] 1 [-257:1084:1]
31850b (2 curves)	1	2+ 5+ 7+ 13+	2+ -1 5+ 7+  0 13+  0  2
Curve Equation t Generators 31850b1 [1,1,0,-11148750,-16713687500] 1 [178500:11942750:27] 31850b2 [1,1,0,-944108750,-11165969847500] 1 [33518100:37317117550:27]
31850c (2 curves)	1	2+ 5+ 7+ 13+	2+  2 5+ 7+  3 13+  3 -1
Curve Equation t Generators 31850c1 [1,1,0,-183823525,959313178125] 1 [-6222841794:-3143554688031:2685619] 31850c2 [1,1,0,24720475,2973595770125] 1 [2306976771166459023540905186:-1830636186567378689030398765561:1049528787366635938705589]
31850d (1 curve)	2	2+ 5+ 7+ 13-	2+ -1 5+ 7+ -4 13-  0 -6
Curve Equation t Generators 31850d1 [1,1,0,-7375,243125] 1 [125:-1200:1]&[-70:685:1]
31850e (4 curves)	0	2+ 5+ 7- 13+	2+  0 5+ 7-  4 13+ -6  0
Curve Equation t 31850e1 [1,-1,0,1061233,-285891859] 2 31850e2 [1,-1,0,-5210767,-2512451859] 4 31850e3 [1,-1,0,-38334767,89605392141] 2 31850e4 [1,-1,0,-72438767,-237205399859] 2
31850f (1 curve)	0	2+ 5+ 7- 13+	2+  1 5+ 7- -1 13+  3  3
Curve Equation t 31850f1 [1,0,1,-8601,631068] 1
31850g (1 curve)	0	2+ 5+ 7- 13+	2+  1 5+ 7- -1 13+  4  0
Curve Equation t 31850g1 [1,0,1,-101876,13830898] 1
31850h (1 curve)	0	2+ 5+ 7- 13+	2+  1 5+ 7-  3 13+  0 -8
Curve Equation t 31850h1 [1,0,1,-5377776,4801215948] 1
31850i (1 curve)	0	2+ 5+ 7- 13+	2+  1 5+ 7- -4 13+  0  6
Curve Equation t 31850i1 [1,0,1,-361401,-84476052] 1
31850j (1 curve)	0	2+ 5+ 7- 13+	2+  1 5+ 7- -5 13+ -8  8
Curve Equation t 31850j1 [1,0,1,-2479426,-1502918252] 1
31850k (1 curve)	0	2+ 5+ 7- 13+	2+ -1 5+ 7-  1 13+ -7  3
Curve Equation t 31850k1 [1,1,0,14675,-7547875] 1
31850l (1 curve)	0	2+ 5+ 7- 13+	2+ -1 5+ 7- -5 13+  2  6
Curve Equation t 31850l1 [1,1,0,-240125,-253527875] 1
31850m (2 curves)	0	2+ 5+ 7- 13+	2+  2 5+ 7- -2 13+  2 -6
Curve Equation t 31850m1 [1,1,0,-1030250,402012500] 2 31850m2 [1,1,0,-932250,481686500] 2
31850n (2 curves)	0	2+ 5+ 7- 13+	2+ -2 5+ 7-  4 13+  4  2
Curve Equation t 31850n1 [1,0,1,7324,3966498] 2 31850n2 [1,0,1,-335676,72566498] 2
31850o (2 curves)	0	2+ 5+ 7- 13+	2+ -2 5+ 7- -4 13+  0  6
Curve Equation t 31850o1 [1,0,1,-1402651,-519779802] 2 31850o2 [1,0,1,-6890651,6493884198] 2
31850p (1 curve)	0	2+ 5+ 7- 13+	2+  3 5+ 7-  1 13+  0  6
Curve Equation t 31850p1 [1,-1,0,4058,166466] 1
31850q (2 curves)	0	2+ 5+ 7- 13+	2+ -3 5+ 7- -2 13+ -3 -6
Curve Equation t 31850q1 [1,-1,0,-3292,-110384] 1 31850q2 [1,-1,0,-260542,56227366] 1
31850r (4 curves)	1	2+ 5+ 7- 13-	2+  0 5+ 7-  0 13-  2  8
Curve Equation t Generators 31850r1 [1,-1,0,-8192,105216] 2 [-61:643:1] 31850r2 [1,-1,0,-106192,13335216] 4 [-12:3828:1] 31850r3 [1,-1,0,-81692,19631716] 2 [39:-4082:1] 31850r4 [1,-1,0,-1698692,852582716] 2 [674:3338:1]
31850s (1 curve)	1	2+ 5+ 7- 13-	2+  0 5+ 7-  6 13-  1  0
Curve Equation t Generators 31850s1 [1,-1,0,-1367,-1709] 1 [-15:131:1]
31850t (2 curves)	1	2+ 5+ 7- 13-	2+  0 5+ 7- -6 13- -8  0
Curve Equation t Generators 31850t1 [1,-1,0,-41524667,-94773503259] 2 [-2875:30421:1] 31850t2 [1,-1,0,46283333,-442229759259] 2 [6059:243158:1]
31850u (2 curves)	1	2+ 5+ 7- 13-	2+  1 5+ 7-  0 13-  0 -2
Curve Equation t Generators 31850u1 [1,0,1,-227526,48695448] 1 [1461:52517:1] 31850u2 [1,0,1,-19267526,32551095448] 1 [2533:-1371:1]
31850v (3 curves)	1	2+ 5+ 7- 13-	2+  1 5+ 7- -3 13-  0 -2
Curve Equation t Generators 31850v1 [1,0,1,8549,325798] 1 [46:4873:8] 31850v2 [1,0,1,-236451,44523798] 1 [522:7701:1] 31850v3 [1,0,1,-19187201,32347749298] 1 [68484:-16493:27]
31850w (1 curve)	1	2+ 5+ 7- 13-	2+ -1 5+ 7-  1 13- -3 -1
Curve Equation t Generators 31850w1 [1,1,0,-136980,-42826160] 1 [47956:1039175:64]
31850x (1 curve)	1	2+ 5+ 7- 13-	2+ -1 5+ 7- -1 13- -4  0
Curve Equation t Generators 31850x1 [1,1,0,-4991900,-4748990000] 1 [36525:6948925:1]
31850y (1 curve)	1	2+ 5+ 7- 13-	2+ -1 5+ 7-  3 13-  0  8
Curve Equation t Generators 31850y1 [1,1,0,-109750,-14044750] 1 [8315:753505:1]
31850z (1 curve)	1	2+ 5+ 7- 13-	2+ -1 5+ 7- -5 13-  8 -8
Curve Equation t Generators 31850z1 [1,1,0,-50600,4360000] 1 [125:25:1]
31850ba (2 curves)	1	2+ 5+ 7- 13-	2+  2 5+ 7-  4 13-  0  2
Curve Equation t Generators 31850ba1 [1,1,0,-7375,-75375] 2 [-162:2139:8] 31850ba2 [1,1,0,-93125,-10965625] 2 [46900:1112425:64]
31850bb (2 curves)	1	2+ 5+ 7- 13-	2+  2 5+ 7-  4 13- -4 -2
Curve Equation t Generators 31850bb1 [1,1,0,150,-11500] 2 [524:11750:1] 31850bb2 [1,1,0,-6850,-214500] 2 [105:435:1]
31850bc (6 curves)	1	2+ 5+ 7- 13-	2+ -2 5+ 7-  0 13-  0 -2
Curve Equation t Generators 31850bc1 [1,0,1,-1465126,-680105352] 2 [-5386:11607:8] 31850bc2 [1,0,1,-23417126,-43618217352] 2 [919668:102482259:64] 31850bc3 [1,0,1,-8129126,8412726648] 2 [-444:109467:1] 31850bc4 [1,0,1,-24936126,-37638453352] 2 [-1844:46467:1] 31850bc5 [1,0,1,-647995626,6348959120648] 2 [14256:84967:1] 31850bc6 [1,0,1,-648081376,6347194728648] 2 [383862:2075359:27]
31850bd (2 curves)	1	2+ 5+ 7- 13-	2+ -2 5+ 7-  3 13- -3  1
Curve Equation t Generators 31850bd1 [1,0,1,-3751501,-2797367352] 1 [29923:5150094:1] 31850bd2 [1,0,1,504499,-8669303352] 1 [3891:-230434:1]
31850be (2 curves)	1	2+ 5+ 7- 13-	2+ -2 5+ 7- -3 13-  3  4
Curve Equation t Generators 31850be1 [1,0,1,-6396,248378] 1 [-79:551:1] 31850be2 [1,0,1,-555196,159180858] 1 [433:-113:1]
31850bf (1 curve)	1	2+ 5+ 7- 13-	2+  3 5+ 7- -3 13- -7 -1
Curve Equation t Generators 31850bf1 [1,-1,0,-1087,-13609] 1 [5115:66557:27]
31850bg (1 curve)	1	2+ 5+ 7- 13-	2+ -3 5+ 7-  3 13- -2  6
Curve Equation t Generators 31850bg1 [1,-1,0,-40042,-3123884] 1 [289:2918:1]
31850bh (1 curve)	1	2+ 5- 7+ 13-	2+ -1 5- 7+ -4 13- -6 -2
Curve Equation t Generators 31850bh1 [1,1,0,72495,11807125] 1 [706:20031:1]
31850bi (2 curves)	1	2+ 5- 7- 13+	2+  0 5- 7-  0 13+ -2  2
Curve Equation t Generators 31850bi1 [1,-1,0,-8927,-214019] 2 [-75:209:1] 31850bi2 [1,-1,0,25373,-1483119] 2 [65:629:1]
31850bj (1 curve)	1	2+ 5- 7- 13+	2+  1 5- 7- -4 13+  6  2
Curve Equation t Generators 31850bj1 [1,0,1,1479,-34212] 1 [27:146:1]
31850bk (2 curves)	1	2+ 5- 7- 13+	2+  2 5- 7-  3 13+ -3  4
Curve Equation t Generators 31850bk1 [1,1,0,-1250,-17800] 1 [2506:124216:1] 31850bk2 [1,1,0,4875,-80275] 1 [50:515:1]
31850bl (2 curves)	1	2+ 5- 7- 13+	2+ -2 5- 7-  2 13+  2  0
Curve Equation t Generators 31850bl1 [1,0,1,-58826,-4978452] 2 [-164:596:1] 31850bl2 [1,0,1,-916326,-337688452] 2 [3102:161761:1]
31850bm (2 curves)	1	2+ 5- 7- 13+	2+ -2 5- 7- -4 13+  0 -4
Curve Equation t Generators 31850bm1 [1,0,1,-64951,-4353702] 2 [-129:1436:1] 31850bm2 [1,0,1,180049,-29343702] 2 [552:15161:1]
31850bn (2 curves)	0	2- 5+ 7+ 13+	2-  2 5+ 7+ -3 13+  3 -7
Curve Equation t 31850bn1 [1,1,1,-9213,434531] 1 31850bn2 [1,1,1,70412,-4502219] 1
31850bo (1 curve)	1	2- 5+ 7+ 13-	2-  0 5+ 7+  1 13-  1  5
Curve Equation t Generators 31850bo1 [1,-1,1,-2680,-834053] 1 [109:345:1]
31850bp (2 curves)	1	2- 5+ 7- 13+	2-  0 5+ 7-  0 13+  6  4
Curve Equation t Generators 31850bp1 [1,-1,1,120,-1753] 2 [905:26763:1] 31850bp2 [1,-1,1,-1630,-22753] 2 [382:455:8]
31850bq (1 curve)	1	2- 5+ 7- 13+	2-  0 5+ 7-  1 13+ -1 -5
Curve Equation t Generators 31850bq1 [1,-1,1,-55,2447] 1 [-1:50:1]
31850br (2 curves)	1	2- 5+ 7- 13+	2-  0 5+ 7- -2 13+ -4  4
Curve Equation t Generators 31850br1 [1,-1,1,-35755,2336247] 2 [39:980:1] 31850br2 [1,-1,1,49995,11768747] 2 [3742:91875:8]
31850bs (4 curves)	1	2- 5+ 7- 13+	2-  0 5+ 7-  4 13+  2  4
Curve Equation t Generators 31850bs1 [1,-1,1,-2450230,-1349948603] 2 [-761:8955:1] 31850bs2 [1,-1,1,-8722230,8409283397] 4 [2823:77821:1] 31850bs3 [1,-1,1,15777770,47119283397] 2 [322473:37437025:27] 31850bs4 [1,-1,1,-133574230,594214867397] 2 [185421:645167:27]
31850bt (1 curve)	1	2- 5+ 7- 13+	2-  1 5+ 7-  1 13+  4 -4
Curve Equation t Generators 31850bt1 [1,0,0,-113,1217] 1 [32:159:1]
31850bu (1 curve)	1	2- 5+ 7- 13+	2-  3 5+ 7- -5 13+ -4 -2
Curve Equation t Generators 31850bu1 [1,-1,1,-27180,-37657553] 1 [9903:29335:27]
31850bv (2 curves)	0	2- 5+ 7- 13-	2-  0 5+ 7-  0 13- -6 -4
Curve Equation t 31850bv1 [1,-1,1,5895,589397] 2 31850bv2 [1,-1,1,-79855,7963897] 2
31850bw (1 curve)	0	2- 5+ 7- 13-	2-  1 5+ 7- -1 13-  4 -2
Curve Equation t 31850bw1 [1,0,0,-5645438,-5172408508] 1
31850bx (3 curves)	0	2- 5+ 7- 13-	2-  1 5+ 7- -3 13-  6 -2
Curve Equation t 31850bx1 [1,0,0,-708598213,-7872487099583] 1 31850bx2 [1,0,0,4363667412,7221331259792] 1 31850bx3 [1,0,0,-61866416963,6281337194900417] 1
31850by (2 curves)	0	2- 5+ 7- 13-	2-  1 5+ 7- -3 13- -6 -2
Curve Equation t 31850by1 [1,0,0,7937,-1787633] 1 31850by2 [1,0,0,-71688,49251992] 1
31850bz (3 curves)	0	2- 5+ 7- 13-	2-  1 5+ 7-  6 13- -3 -2
Curve Equation t 31850bz1 [1,0,0,587,-8933] 1 31850bz2 [1,0,0,-5538,315692] 1 31850bz3 [1,0,0,-562913,162511817] 1
31850ca (1 curve)	0	2- 5+ 7- 13-	2- -1 5+ 7-  1 13- -4  4
Curve Equation t 31850ca1 [1,1,1,-5538,-422969] 1
31850cb (4 curves)	0	2- 5+ 7- 13-	2- -2 5+ 7-  0 13-  0 -2
Curve Equation t 31850cb1 [1,0,0,-286063,-58835883] 2 31850cb2 [1,0,0,-371813,-20677133] 2 31850cb3 [1,0,0,-1161938,424567492] 2 31850cb4 [1,0,0,-17968938,29315800492] 2
31850cc (2 curves)	0	2- 5+ 7- 13-	2- -2 5+ 7-  3 13-  3  4
Curve Equation t 31850cc1 [1,0,0,-31263,-2162483] 1 31850cc2 [1,0,0,121862,-10278108] 1
31850cd (2 curves)	0	2- 5+ 7- 13-	2- -2 5+ 7- -3 13- -3  7
Curve Equation t 31850cd1 [1,0,0,-451438,-150398508] 1 31850cd2 [1,0,0,3450187,1554611617] 1
31850ce (4 curves)	2	2- 5+ 7- 13-	2- -2 5+ 7- -6 13- -6 -2
Curve Equation t Generators 31850ce1 [1,0,0,-39838,-3045708] 2 [-122:110:1]&[382:-6316:1] 31850ce2 [1,0,0,-15338,-6745208] 2 [228:1160:1]&[372:-6436:1] 31850ce3 [1,0,0,-254213,47332417] 2 [1642:-64521:1]&[82:5159:1] 31850ce4 [1,0,0,137787,180220417] 2 [312:-16081:1]&[-338:9919:1]
31850cf (1 curve)	1	2- 5- 7+ 13+	2-  1 5- 7+ -4 13+  6 -2
Curve Equation t Generators 31850cf1 [1,0,0,1812362,1472265892] 1 [-498:21374:1]
31850cg (1 curve)	0	2- 5- 7+ 13-	2-  0 5- 7+  6 13-  1  0
Curve Equation t 31850cg1 [1,-1,1,-2680,6297] 1
31850ch (1 curve)	0	2- 5- 7- 13+	2-  0 5- 7-  6 13+ -1  0
Curve Equation t 31850ch1 [1,-1,1,-55,-3] 1
31850ci (1 curve)	0	2- 5- 7- 13+	2-  1 5- 7-  1 13+  3 -1
Curve Equation t 31850ci1 [1,0,0,-3424513,-5346420983] 1
31850cj (2 curves)	0	2- 5- 7- 13+	2-  2 5- 7- -3 13+ -3  4
Curve Equation t 31850cj1 [1,1,1,-159888,31047281] 1 31850cj2 [1,1,1,-13879888,19897607281] 1
31850ck (1 curve)	0	2- 5- 7- 13+	2- -3 5- 7- -3 13+  7 -1
Curve Equation t 31850ck1 [1,-1,1,-27180,-1728303] 1
31850cl (2 curves)	1	2- 5- 7- 13-	2-  0 5- 7-  0 13-  2  2
Curve Equation t Generators 31850cl1 [1,-1,1,-223180,-26975553] 2 [-381:1815:1] 31850cl2 [1,-1,1,634320,-184755553] 2 [305:5931:1]
31850cm (1 curve)	1	2- 5- 7- 13-	2-  1 5- 7-  1 13-  7  3
Curve Equation t Generators 31850cm1 [1,0,0,587,-60383] 1 [186:2455:1]
31850cn (1 curve)	1	2- 5- 7- 13-	2- -1 5- 7- -1 13- -3  3
Curve Equation t Generators 31850cn1 [1,1,1,-215013,78883531] 1 [685:-16268:1]
31850co (1 curve)	1	2- 5- 7- 13-	2- -1 5- 7- -4 13- -6  2
Curve Equation t Generators 31850co1 [1,1,1,36987,-4276469] 1 [535:12732:1]
31850cp (2 curves)	1	2- 5- 7- 13-	2-  2 5- 7-  2 13- -2  0
Curve Equation t Generators 31850cp1 [1,1,1,-2353,-40769] 2 [-35:32:1] 31850cp2 [1,1,1,-36653,-2716169] 2 [-3003:1550:27]
31850cq (2 curves)	1	2- 5- 7- 13-	2-  2 5- 7- -4 13-  0 -4
Curve Equation t Generators 31850cq1 [1,1,1,-2598,-35869] 2 [111:973:1] 31850cq2 [1,1,1,7202,-231869] 2 [175:2447:1]

Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
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