Cremona's table of elliptic curves

31248 = 2⁴ · 3² · 7 · 31

Class	r	Atkin-Lehner	Eigenvalues
31248a (1 curve)	0	2+ 3+ 7+ 31-	2+ 3+  3 7+ -4 -5 -2  8
Curve Equation t 31248a1 [0,0,0,324,10908] 1
31248b (1 curve)	0	2+ 3+ 7+ 31-	2+ 3+ -3 7+  4 -5  2  8
Curve Equation t 31248b1 [0,0,0,36,-404] 1
31248c (2 curves)	0	2+ 3+ 7+ 31-	2+ 3+  4 7+  0 -6  2  4
Curve Equation t 31248c1 [0,0,0,-1518,22815] 2 31248c2 [0,0,0,-24303,1458270] 2
31248d (2 curves)	0	2+ 3+ 7+ 31-	2+ 3+ -4 7+  0 -6 -2  4
Curve Equation t 31248d1 [0,0,0,-13662,-616005] 2 31248d2 [0,0,0,-218727,-39373290] 2
31248e (1 curve)	0	2+ 3+ 7- 31+	2+ 3+  3 7-  1  1  3 -5
Curve Equation t 31248e1 [0,0,0,-6291,-209358] 1
31248f (1 curve)	2	2+ 3+ 7- 31+	2+ 3+ -3 7- -1  1 -3 -5
Curve Equation t Generators 31248f1 [0,0,0,-699,7754] 1 [17:28:1]&[-23:108:1]
31248g (2 curves)	1	2+ 3+ 7- 31-	2+ 3+  4 7- -4 -2  2 -4
Curve Equation t Generators 31248g1 [0,0,0,162,-5805] 2 [4295:25102:125] 31248g2 [0,0,0,-4023,-93690] 2 [145:1540:1]
31248h (2 curves)	1	2+ 3+ 7- 31-	2+ 3+ -4 7-  4 -2 -2 -4
Curve Equation t Generators 31248h1 [0,0,0,18,215] 2 [-1:14:1] 31248h2 [0,0,0,-447,3470] 2 [-11:84:1]
31248i (2 curves)	2	2+ 3- 7+ 31+	2+ 3-  0 7+ -2 -6 -2 -4
Curve Equation t Generators 31248i1 [0,0,0,-615,5798] 2 [-14:108:1]&[1:72:1] 31248i2 [0,0,0,-75,15626] 2 [-23:72:1]&[5:-124:1]
31248j (2 curves)	1	2+ 3- 7+ 31-	2+ 3-  0 7+ -2 -2  2 -4
Curve Equation t Generators 31248j1 [0,0,0,-31575,2158774] 2 [-142:1944:1] 31248j2 [0,0,0,-26715,2845978] 2 [77:-1116:1]
31248k (1 curve)	1	2+ 3- 7+ 31-	2+ 3-  1 7+  3 -3 -1  5
Curve Equation t Generators 31248k1 [0,0,0,9573,79018] 1 [209:-3348:1]
31248l (2 curves)	1	2+ 3- 7+ 31-	2+ 3-  2 7+  0 -2  6 -6
Curve Equation t Generators 31248l1 [0,0,0,-579,-5038] 2 [-14:18:1] 31248l2 [0,0,0,501,-21670] 2 [58:450:1]
31248m (4 curves)	1	2+ 3- 7+ 31-	2+ 3- -2 7+  4  2  2 -4
Curve Equation t Generators 31248m1 [0,0,0,-426,-2329] 2 [1893:15092:27] 31248m2 [0,0,0,-2631,50150] 4 [22:54:1] 31248m3 [0,0,0,1149,182450] 4 [274:4590:1] 31248m4 [0,0,0,-41691,3276506] 2 [91:486:1]
31248n (2 curves)	1	2+ 3- 7+ 31-	2+ 3- -2 7+ -6  0 -4  4
Curve Equation t Generators 31248n1 [0,0,0,9,-810] 2 [18:72:1] 31248n2 [0,0,0,-1251,-16686] 2 [-21:18:1]
31248o (2 curves)	1	2+ 3- 7- 31+	2+ 3-  0 7-  2 -2  2 -2
Curve Equation t Generators 31248o1 [0,0,0,-2595,-11342] 2 [-43:144:1] 31248o2 [0,0,0,-31755,-2175014] 2 [762:20398:1]
31248p (2 curves)	1	2+ 3- 7- 31+	2+ 3-  0 7-  2 -2  6 -8
Curve Equation t Generators 31248p1 [0,0,0,-570,7859] 2 [55:378:1] 31248p2 [0,0,0,-10335,404318] 2 [46:162:1]
31248q (1 curve)	1	2+ 3- 7- 31+	2+ 3- -1 7-  3 -1 -1 -3
Curve Equation t Generators 31248q1 [0,0,0,-4493523,-7854375566] 1 [38146:2250423:8]
31248r (4 curves)	1	2+ 3- 7- 31+	2+ 3-  2 7-  0  2  2  0
Curve Equation t Generators 31248r1 [0,0,0,-759,-7562] 2 [81:680:1] 31248r2 [0,0,0,-2379,35530] 4 [-37:270:1] 31248r3 [0,0,0,5181,215458] 2 [-9:410:1] 31248r4 [0,0,0,-35859,2613490] 2 [117:140:1]
31248s (2 curves)	1	2+ 3- 7- 31+	2+ 3- -2 7-  2 -4  0  4
Curve Equation t Generators 31248s1 [0,0,0,-112311,-62010090] 2 [517:4256:1] 31248s2 [0,0,0,-3137571,-2133103086] 2 [-981:882:1]
31248t (1 curve)	1	2+ 3- 7- 31+	2+ 3-  3 7-  0  3  4 -6
Curve Equation t Generators 31248t1 [0,0,0,83364,-95873668] 1 [28514:1706103:8]
31248u (1 curve)	0	2+ 3- 7- 31-	2+ 3- -1 7-  0 -7 -8  6
Curve Equation t 31248u1 [0,0,0,-2028,-35156] 1
31248v (1 curve)	0	2+ 3- 7- 31-	2+ 3- -1 7-  4  4 -2  2
Curve Equation t 31248v1 [0,0,0,-3,866] 1
31248w (4 curves)	0	2+ 3- 7- 31-	2+ 3-  2 7-  4 -2 -2  8
Curve Equation t 31248w1 [0,0,0,-9399,-270538] 2 31248w2 [0,0,0,-140619,-20294710] 4 31248w3 [0,0,0,-130899,-23220430] 2 31248w4 [0,0,0,-2249859,-1298915998] 2
31248x (2 curves)	0	2+ 3- 7- 31-	2+ 3-  4 7-  6 -6  6 -6
Curve Equation t 31248x1 [0,0,0,-33843,-2371070] 2 31248x2 [0,0,0,-63003,2323690] 2
31248y (2 curves)	0	2+ 3- 7- 31-	2+ 3- -4 7-  6  2 -2  0
Curve Equation t 31248y1 [0,0,0,78,17575] 2 31248y2 [0,0,0,-9687,359350] 2
31248z (1 curve)	1	2- 3+ 7+ 31-	2- 3+  1 7+  5 -1 -5 -1
Curve Equation t Generators 31248z1 [0,0,0,-55395387,-162180887958] 1 [17756104128937868685:-9308947628534158067778:64553588520875]
31248ba (1 curve)	1	2- 3+ 7+ 31-	2- 3+ -1 7+ -5 -1  5 -1
Curve Equation t Generators 31248ba1 [0,0,0,-6155043,6006699554] 1 [2737:98304:1]
31248bb (2 curves)	1	2- 3+ 7+ 31-	2- 3+  2 7+  4 -4  2 -4
Curve Equation t Generators 31248bb1 [0,0,0,-24,23] 2 [29:154:1] 31248bb2 [0,0,0,81,170] 2 [226:1265:8]
31248bc (2 curves)	1	2- 3+ 7+ 31-	2- 3+ -2 7+ -4 -4 -2 -4
Curve Equation t Generators 31248bc1 [0,0,0,-216,-621] 2 [25:98:1] 31248bc2 [0,0,0,729,-4590] 2 [146:973:8]
31248bd (2 curves)	0	2- 3+ 7- 31-	2- 3+  2 7- -6 -2  8  4
Curve Equation t 31248bd1 [0,0,0,-1944,33507] 2 31248bd2 [0,0,0,-31239,2125170] 2
31248be (2 curves)	0	2- 3+ 7- 31-	2- 3+ -2 7-  6 -2 -8  4
Curve Equation t 31248be1 [0,0,0,-216,-1241] 2 31248be2 [0,0,0,-3471,-78710] 2
31248bf (1 curve)	0	2- 3+ 7- 31-	2- 3+  3 7-  4  1 -2  0
Curve Equation t 31248bf1 [0,0,0,-96,432] 1
31248bg (1 curve)	0	2- 3+ 7- 31-	2- 3+ -3 7- -4  1  2  0
Curve Equation t 31248bg1 [0,0,0,-864,-11664] 1
31248bh (4 curves)	1	2- 3- 7+ 31+	2- 3-  0 7+  0 -4  6  4
Curve Equation t Generators 31248bh1 [0,0,0,-3540,-62557] 2 [-140528:557289:4096] 31248bh2 [0,0,0,-18975,953066] 2 [-98:1368:1] 31248bh3 [0,0,0,-268140,-53442961] 2 [2439980907737483:-63432166343080304:2444553286111] 31248bh4 [0,0,0,-268455,-53311102] 2 [-112848218:152276184:389017]
31248bi (4 curves)	1	2- 3- 7+ 31+	2- 3-  0 7+  6  2 -6  4
Curve Equation t Generators 31248bi1 [0,0,0,-26715,1402634] 2 [-182:486:1] 31248bi2 [0,0,0,51045,8043338] 2 [157:-4464:1] 31248bi3 [0,0,0,-616395,-186124678] 2 [1313983:17225728:1331] 31248bi4 [0,0,0,-478155,-271861126] 2 [1733:64064:1]
31248bj (2 curves)	1	2- 3- 7+ 31+	2- 3- -2 7+  0 -6  2  2
Curve Equation t Generators 31248bj1 [0,0,0,-27291,-1527734] 2 [-121:54:1] 31248bj2 [0,0,0,41829,-8011190] 2 [413:-8928:1]
31248bk (3 curves)	1	2- 3- 7+ 31+	2- 3-  3 7+  0  5  0 -2
Curve Equation t Generators 31248bk1 [0,0,0,3264,-156112] 1 [17864:8019:512] 31248bk2 [0,0,0,-152256,-22908688] 1 [2822014072:6481822149:6229504] 31248bk3 [0,0,0,-12338976,-16682717392] 1 [15628438293994687931929454984:-321663956900603965324859129211:3677068632775762741064192]
31248bl (3 curves)	1	2- 3- 7+ 31+	2- 3- -3 7+  0 -4  6 -2
Curve Equation t Generators 31248bl1 [0,0,0,-579,28226] 1 [-31:128:1] 31248bl2 [0,0,0,5181,-737854] 1 [113:1136:1] 31248bl3 [0,0,0,-485859,-130417054] 1 [91625:27733736:1]
31248bm (2 curves)	1	2- 3- 7+ 31+	2- 3- -3 7+ -3 -1 -3  1
Curve Equation t Generators 31248bm1 [0,0,0,10581,9324506] 1 [295:6174:1] 31248bm2 [0,0,0,-95259,-252206134] 1 [799:13482:1]
31248bn (1 curve)	0	2- 3- 7+ 31-	2- 3- -1 7+  1  5  5  5
Curve Equation t 31248bn1 [0,0,0,-33123,-2320414] 1
31248bo (2 curves)	0	2- 3- 7+ 31-	2- 3-  2 7+  0 -2  6 -2
Curve Equation t 31248bo1 [0,0,0,-1353099,-546000838] 2 31248bo2 [0,0,0,1796181,-2710815910] 2
31248bp (4 curves)	0	2- 3- 7+ 31-	2- 3-  2 7+  0 -6 -6  4
Curve Equation t 31248bp1 [0,0,0,5181,-145150] 2 31248bp2 [0,0,0,-30099,-1379950] 4 31248bp3 [0,0,0,-186339,29899298] 2 31248bp4 [0,0,0,-438339,-111686398] 2
31248bq (2 curves)	0	2- 3- 7+ 31-	2- 3-  2 7+  2  4 -8  4
Curve Equation t 31248bq1 [0,0,0,-805899,-279440390] 2 31248bq2 [0,0,0,-12906939,-17847730262] 2
31248br (2 curves)	0	2- 3- 7+ 31-	2- 3-  2 7+ -2 -4  2  8
Curve Equation t 31248br1 [0,0,0,3021,81650] 2 31248br2 [0,0,0,-20019,823538] 2
31248bs (2 curves)	0	2- 3- 7+ 31-	2- 3-  2 7+ -6  4  0  4
Curve Equation t 31248bs1 [0,0,0,-4539,195050] 2 31248bs2 [0,0,0,-85179,9565418] 2
31248bt (2 curves)	2	2- 3- 7+ 31-	2- 3- -4 7+  2 -2 -2 -8
Curve Equation t Generators 31248bt1 [0,0,0,-507,2410] 2 [-22:54:1]&[-19:72:1] 31248bt2 [0,0,0,1653,17530] 2 [21:-248:1]&[-3:112:1]
31248bu (2 curves)	0	2- 3- 7+ 31-	2- 3- -4 7+ -2  2  8 -4
Curve Equation t 31248bu1 [0,0,0,38868,-3917905] 2 31248bu2 [0,0,0,-263847,-39940990] 2
31248bv (2 curves)	2	2- 3- 7- 31+	2- 3-  0 7- -6 -2 -6 -6
Curve Equation t Generators 31248bv1 [0,0,0,-1515,5402] 2 [-38:90:1]&[-17:162:1] 31248bv2 [0,0,0,-14475,-665926] 2 [-67:56:1]&[-65:18:1]
31248bw (1 curve)	2	2- 3- 7- 31+	2- 3- -1 7- -5 -5  3  1
Curve Equation t Generators 31248bw1 [0,0,0,-3,15874] 1 [17:-144:1]&[-15:112:1]
31248bx (4 curves)	0	2- 3- 7- 31+	2- 3-  2 7-  0  2 -6 -4
Curve Equation t 31248bx1 [0,0,0,-287859,-59443918] 2 31248bx2 [0,0,0,-299379,-54428110] 4 31248bx3 [0,0,0,504141,-296287630] 2 31248bx4 [0,0,0,-1287219,508443122] 2
31248by (2 curves)	0	2- 3- 7- 31+	2- 3-  2 7- -2  4  0  4
Curve Equation t 31248by1 [0,0,0,4115301,276025930] 2 31248by2 [0,0,0,-16528539,2212418122] 2
31248bz (2 curves)	0	2- 3- 7- 31+	2- 3-  2 7- -2 -4  0  4
Curve Equation t 31248bz1 [0,0,0,501,-8710] 2 31248bz2 [0,0,0,-4539,-100438] 2
31248ca (6 curves)	0	2- 3- 7- 31+	2- 3-  2 7-  4 -2  6  4
Curve Equation t 31248ca1 [0,0,0,-14979,-83793278] 2 31248ca2 [0,0,0,-2964099,-1937610110] 4 31248ca3 [0,0,0,-5867139,2480236162] 2 31248ca4 [0,0,0,-47246979,-124999733630] 4 31248ca5 [0,0,0,-47068419,-125991420158] 2 31248ca6 [0,0,0,-755951619,-7999983952382] 2
31248cb (4 curves)	0	2- 3- 7- 31+	2- 3- -2 7-  4  2  2  0
Curve Equation t 31248cb1 [0,0,0,-6051,-180574] 2 31248cb2 [0,0,0,-8931,8930] 4 31248cb3 [0,0,0,35709,71426] 2 31248cb4 [0,0,0,-99651,12074690] 2
31248cc (1 curve)	2	2- 3- 7- 31+	2- 3- -3 7-  0 -5  0 -6
Curve Equation t Generators 31248cc1 [0,0,0,816,181676] 1 [-50:126:1]&[62:686:1]
31248cd (2 curves)	2	2- 3- 7- 31+	2- 3- -4 7- -2 -2 -6 -2
Curve Equation t Generators 31248cd1 [0,0,0,-1566507,754639450] 2 [82945:338688:125]&[-1003:36288:1] 31248cd2 [0,0,0,-1618347,702021850] 2 [1637:49392:1]&[-1009:36162:1]
31248ce (2 curves)	1	2- 3- 7- 31-	2- 3-  0 7-  0  0  2  4
Curve Equation t Generators 31248ce1 [0,0,0,-300,-1969] 2 [437:9128:1] 31248ce2 [0,0,0,-615,2882] 2 [-26:36:1]
31248cf (2 curves)	1	2- 3- 7- 31-	2- 3-  0 7-  2  2 -2  2
Curve Equation t Generators 31248cf1 [0,0,0,-916635,298547786] 2 [367:3402:1] 31248cf2 [0,0,0,-14187675,20568734282] 2 [2749:48384:1]
31248cg (2 curves)	1	2- 3- 7- 31-	2- 3-  0 7- -2 -2 -2  6
Curve Equation t Generators 31248cg1 [0,0,0,-1035,-8262] 2 [-9:18:1] 31248cg2 [0,0,0,-6795,209466] 2 [85:-496:1]
31248ch (2 curves)	1	2- 3- 7- 31-	2- 3-  0 7- -4 -4 -2 -4
Curve Equation t Generators 31248ch1 [0,0,0,-204420,-35571013] 2 [14403:72352:27] 31248ch2 [0,0,0,-219855,-29887846] 2 [-242:3024:1]
31248ci (1 curve)	1	2- 3- 7- 31-	2- 3-  1 7-  0  1  4 -2
Curve Equation t Generators 31248ci1 [0,0,0,-192,-1892] 1 [18:22:1]
31248cj (4 curves)	1	2- 3- 7- 31-	2- 3- -2 7-  0 -2 -2 -8
Curve Equation t Generators 31248cj1 [0,0,0,-523731,141900946] 2 [-34:12636:1] 31248cj2 [0,0,0,-1261011,-346325870] 4 [86148:1272271:64] 31248cj3 [0,0,0,3738669,-2411193710] 2 [62758476:2322145085:85184] 31248cj4 [0,0,0,-18057171,-29527974254] 2 [5330:160146:1]
31248ck (2 curves)	1	2- 3- 7- 31-	2- 3- -2 7- -6  4 -2  4
Curve Equation t Generators 31248ck1 [0,0,0,-4611,128770] 2 [33:-112:1] 31248ck2 [0,0,0,-75171,7932706] 2 [-121:3906:1]
31248cl (1 curve)	1	2- 3- 7- 31-	2- 3-  3 7- -3 -3  5  1
Curve Equation t Generators 31248cl1 [0,0,0,-180291,32500802] 1 [353:3584:1]
31248cm (1 curve)	1	2- 3- 7- 31-	2- 3-  3 7-  4  4 -2 -6
Curve Equation t Generators 31248cm1 [0,0,0,-340371,-76432302] 1 [2197617832231:-48751501984496:2336752783]

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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