Cremona's table of elliptic curves

43680 = 2⁵ · 3 · 5 · 7 · 13

Class	r	Atkin-Lehner	Eigenvalues
43680a (4 curves)	0	2+ 3+ 5+ 7- 13+	2+ 3+ 5+ 7-  4 13+  2  0
Curve Equation t 43680a1 [0,-1,0,-1106,-11400] 4 43680a2 [0,-1,0,2144,-68600] 2 43680a3 [0,-1,0,-5201,135201] 2 43680a4 [0,-1,0,-16856,-836700] 2
43680b (2 curves)	1	2+ 3+ 5+ 7- 13-	2+ 3+ 5+ 7-  0 13-  2  4
Curve Equation t Generators 43680b1 [0,-1,0,34,36] 2 [0:6:1] 43680b2 [0,-1,0,-161,465] 2 [-11:28:1]
43680c (2 curves)	1	2+ 3+ 5+ 7- 13-	2+ 3+ 5+ 7- -2 13-  0  0
Curve Equation t Generators 43680c1 [0,-1,0,-43646,3523920] 2 [134:-252:1] 43680c2 [0,-1,0,-40216,4097416] 2 [85:1134:1]
43680d (4 curves)	0	2+ 3+ 5- 7+ 13+	2+ 3+ 5- 7+  0 13+  6  4
Curve Equation t 43680d1 [0,-1,0,-21770,323400] 4 43680d2 [0,-1,0,83855,2457025] 2 43680d3 [0,-1,0,-205520,-35544600] 2 43680d4 [0,-1,0,-270200,54083652] 4
43680e (2 curves)	0	2+ 3+ 5- 7+ 13+	2+ 3+ 5- 7+ -2 13+ -2  2
Curve Equation t 43680e1 [0,-1,0,-2099410,1171528600] 2 43680e2 [0,-1,0,-2077440,1197224712] 2
43680f (4 curves)	2	2+ 3+ 5- 7+ 13+	2+ 3+ 5- 7+ -4 13+ -6 -4
Curve Equation t Generators 43680f1 [0,-1,0,-190,-800] 4 [-9:10:1]&[-8:12:1] 43680f2 [0,-1,0,335,-4895] 2 [27:152:1]&[138:605:8] 43680f3 [0,-1,0,-840,8820] 2 [-28:98:1]&[-4:110:1] 43680f4 [0,-1,0,-2920,-59768] 2 [69:250:1]&[113:1020:1]
43680g (2 curves)	1	2+ 3+ 5- 7- 13+	2+ 3+ 5- 7-  0 13+  0 -8
Curve Equation t Generators 43680g1 [0,-1,0,70,-228] 2 [4:10:1] 43680g2 [0,-1,0,-385,-1775] 2 [-15:20:1]
43680h (2 curves)	1	2+ 3+ 5- 7- 13+	2+ 3+ 5- 7-  2 13+ -4  8
Curve Equation t Generators 43680h1 [0,-1,0,-190,1072] 2 [7:6:1] 43680h2 [0,-1,0,-120,1800] 2 [21:90:1]
43680i (4 curves)	0	2+ 3+ 5- 7- 13-	2+ 3+ 5- 7-  0 13-  2  4
Curve Equation t 43680i1 [0,-1,0,-330,1800] 4 43680i2 [0,-1,0,840,10692] 4 43680i3 [0,-1,0,-1905,-30015] 2 43680i4 [0,-1,0,-4880,132840] 2
43680j (4 curves)	0	2+ 3+ 5- 7- 13-	2+ 3+ 5- 7-  4 13-  6  4
Curve Equation t 43680j1 [0,-1,0,-2730,55800] 4 43680j2 [0,-1,0,-2280,74340] 4 43680j3 [0,-1,0,-3185,36417] 2 43680j4 [0,-1,0,-43680,3528360] 2
43680k (2 curves)	0	2+ 3+ 5- 7- 13-	2+ 3+ 5- 7-  6 13- -2  2
Curve Equation t 43680k1 [0,-1,0,-195410,-33176808] 2 43680k2 [0,-1,0,-173440,-40945400] 2
43680l (2 curves)	0	2+ 3- 5+ 7+ 13+	2+ 3- 5+ 7+ -6 13+ -2  6
Curve Equation t 43680l1 [0,1,0,-70866,-7284816] 2 43680l2 [0,1,0,-70736,-7312740] 2
43680m (2 curves)	1	2+ 3- 5+ 7+ 13-	2+ 3- 5+ 7+  2 13-  0  0
Curve Equation t Generators 43680m1 [0,1,0,-43646,-3523920] 2 [241:114:1] 43680m2 [0,1,0,-40216,-4097416] 2 [590:13338:1]
43680n (2 curves)	1	2+ 3- 5+ 7+ 13-	2+ 3- 5+ 7+ -6 13-  6 -2
Curve Equation t Generators 43680n1 [0,1,0,-26,0] 2 [9:24:1] 43680n2 [0,1,0,104,104] 2 [2:18:1]
43680o (2 curves)	1	2+ 3- 5+ 7- 13+	2+ 3- 5+ 7- -2 13+  6 -6
Curve Equation t Generators 43680o1 [0,1,0,-1706,-27696] 2 [57:252:1] 43680o2 [0,1,0,-1576,-31960] 2 [82:630:1]
43680p (2 curves)	1	2+ 3- 5+ 7- 13+	2+ 3- 5+ 7-  4 13+  6  0
Curve Equation t Generators 43680p1 [0,1,0,1234,-47100] 2 [64:546:1] 43680p2 [0,1,0,-14561,-612561] 2 [-65:252:1]
43680q (4 curves)	1	2+ 3- 5+ 7- 13+	2+ 3- 5+ 7-  4 13+ -6  0
Curve Equation t Generators 43680q1 [0,1,0,-37266,2729520] 4 [-48:2100:1] 43680q2 [0,1,0,-8016,6929820] 2 [-9:2646:1] 43680q3 [0,1,0,-68136,-2481336] 2 [435:7098:1] 43680q4 [0,1,0,-594641,176296095] 2 [442:-105:1]
43680r (4 curves)	1	2+ 3- 5+ 7- 13+	2+ 3- 5+ 7- -4 13+ -6 -8
Curve Equation t Generators 43680r1 [0,1,0,-9506,-352800] 4 [-56:84:1] 43680r2 [0,1,0,1024,-1081476] 2 [295:4998:1] 43680r3 [0,1,0,-20881,641375] 2 [-118:1215:1] 43680r4 [0,1,0,-151256,-22692600] 2 [451:1014:1]
43680s (2 curves)	0	2+ 3- 5+ 7- 13-	2+ 3- 5+ 7-  2 13- -2 -2
Curve Equation t 43680s1 [0,1,0,-306,-2160] 2 43680s2 [0,1,0,-176,-3876] 2
43680t (2 curves)	1	2+ 3- 5- 7+ 13+	2+ 3- 5- 7+  0 13+  0  8
Curve Equation t Generators 43680t1 [0,1,0,70,228] 2 [6:30:1] 43680t2 [0,1,0,-385,1775] 2 [35:-180:1]
43680u (2 curves)	1	2+ 3- 5- 7+ 13+	2+ 3- 5- 7+  0 13+ -2  0
Curve Equation t Generators 43680u1 [0,1,0,-8310,432900] 2 [-30:810:1] 43680u2 [0,1,0,-150465,22410063] 2 [231:-180:1]
43680v (2 curves)	1	2+ 3- 5- 7+ 13+	2+ 3- 5- 7+ -2 13+ -4 -8
Curve Equation t Generators 43680v1 [0,1,0,-190,-1072] 2 [17:30:1] 43680v2 [0,1,0,-120,-1800] 2 [30:150:1]
43680w (4 curves)	0	2+ 3- 5- 7+ 13-	2+ 3- 5- 7+  4 13-  2 -8
Curve Equation t 43680w1 [0,1,0,-1450,-11152] 4 43680w2 [0,1,0,4920,-77400] 4 43680w3 [0,1,0,-11200,445148] 2 43680w4 [0,1,0,-19825,-1080577] 2
43680x (4 curves)	0	2+ 3- 5- 7- 13+	2+ 3- 5- 7-  4 13+ -6  4
Curve Equation t 43680x1 [0,1,0,-190,800] 4 43680x2 [0,1,0,335,4895] 2 43680x3 [0,1,0,-840,-8820] 2 43680x4 [0,1,0,-2920,59768] 2
43680y (4 curves)	1	2+ 3- 5- 7- 13-	2+ 3- 5- 7- -4 13- -2 -4
Curve Equation t Generators 43680y1 [0,1,0,-2490,-46512] 4 [-27:42:1] 43680y2 [0,1,0,1560,-179352] 4 [243:3822:1] 43680y3 [0,1,0,-7040,166428] 2 [103:738:1] 43680y4 [0,1,0,-39345,-3017025] 2 [285:3000:1]
43680z (2 curves)	0	2- 3+ 5+ 7+ 13+	2- 3+ 5+ 7+  2 13+  6  6
Curve Equation t 43680z1 [0,-1,0,-1706,27696] 2 43680z2 [0,-1,0,-1576,31960] 2
43680ba (4 curves)	0	2- 3+ 5+ 7+ 13+	2- 3+ 5+ 7+  4 13+ -6  8
Curve Equation t 43680ba1 [0,-1,0,-9506,352800] 4 43680ba2 [0,-1,0,1024,1081476] 2 43680ba3 [0,-1,0,-20881,-641375] 2 43680ba4 [0,-1,0,-151256,22692600] 2
43680bb (2 curves)	0	2- 3+ 5+ 7+ 13+	2- 3+ 5+ 7+ -4 13+  6  0
Curve Equation t 43680bb1 [0,-1,0,1234,47100] 2 43680bb2 [0,-1,0,-14561,612561] 2
43680bc (4 curves)	0	2- 3+ 5+ 7+ 13+	2- 3+ 5+ 7+ -4 13+ -6  0
Curve Equation t 43680bc1 [0,-1,0,-37266,-2729520] 4 43680bc2 [0,-1,0,-8016,-6929820] 2 43680bc3 [0,-1,0,-68136,2481336] 2 43680bc4 [0,-1,0,-594641,-176296095] 2
43680bd (2 curves)	1	2- 3+ 5+ 7+ 13-	2- 3+ 5+ 7+ -2 13- -2  2
Curve Equation t Generators 43680bd1 [0,-1,0,-306,2160] 2 [-16:52:1] 43680bd2 [0,-1,0,-176,3876] 2 [8:-54:1]
43680be (2 curves)	1	2- 3+ 5+ 7+ 13-	2- 3+ 5+ 7+ -6 13- -4 -4
Curve Equation t Generators 43680be1 [0,-1,0,-4646,-119304] 2 [-37:24:1] 43680be2 [0,-1,0,-1216,-294920] 2 [649:16488:1]
43680bf (4 curves)	1	2- 3+ 5+ 7- 13+	2- 3+ 5+ 7- -4 13+ -2 -4
Curve Equation t Generators 43680bf1 [0,-1,0,-1366,-18920] 4 [-21:8:1] 43680bf2 [0,-1,0,-736,-37064] 2 [105:1016:1] 43680bf3 [0,-1,0,-2016,1620] 2 [-36:162:1] 43680bf4 [0,-1,0,-21841,-1235135] 2 [171:32:1]
43680bg (2 curves)	1	2- 3+ 5+ 7- 13+	2- 3+ 5+ 7- -4 13+  4  8
Curve Equation t Generators 43680bg1 [0,-1,0,-3568586,2596166436] 2 [906:10290:1] 43680bg2 [0,-1,0,-57098881,166088393425] 2 [118101:-34300:27]
43680bh (2 curves)	1	2- 3+ 5+ 7- 13+	2- 3+ 5+ 7-  6 13+ -2 -6
Curve Equation t Generators 43680bh1 [0,-1,0,-70866,7284816] 2 [203:1106:1] 43680bh2 [0,-1,0,-70736,7312740] 2 [-64:3402:1]
43680bi (2 curves)	0	2- 3+ 5+ 7- 13-	2- 3+ 5+ 7-  6 13-  6  2
Curve Equation t 43680bi1 [0,-1,0,-26,0] 2 43680bi2 [0,-1,0,104,-104] 2
43680bj (2 curves)	0	2- 3+ 5+ 7- 13-	2- 3+ 5+ 7- -6 13-  0  4
Curve Equation t 43680bj1 [0,-1,0,-215668726,-1218972024344] 2 43680bj2 [0,-1,0,-207433296,-1316357631180] 2
43680bk (4 curves)	0	2- 3+ 5- 7+ 13-	2- 3+ 5- 7+  0 13-  6  4
Curve Equation t 43680bk1 [0,-1,0,-670,5800] 4 43680bk2 [0,-1,0,1280,31540] 2 43680bk3 [0,-1,0,-3120,-60840] 2 43680bk4 [0,-1,0,-10225,401377] 4
43680bl (4 curves)	0	2- 3+ 5- 7+ 13-	2- 3+ 5- 7+  4 13- -2  4
Curve Equation t 43680bl1 [0,-1,0,-2490,46512] 4 43680bl2 [0,-1,0,1560,179352] 2 43680bl3 [0,-1,0,-7040,-166428] 2 43680bl4 [0,-1,0,-39345,3017025] 4
43680bm (2 curves)	0	2- 3+ 5- 7- 13+	2- 3+ 5- 7-  0 13+  0  0
Curve Equation t 43680bm1 [0,-1,0,-178290,73811412] 2 43680bm2 [0,-1,0,-3946145,3014999025] 2
43680bn (2 curves)	0	2- 3+ 5- 7- 13+	2- 3+ 5- 7-  0 13+ -2  0
Curve Equation t 43680bn1 [0,-1,0,-8310,-432900] 2 43680bn2 [0,-1,0,-150465,-22410063] 2
43680bo (2 curves)	0	2- 3+ 5- 7- 13+	2- 3+ 5- 7-  2 13+  0  4
Curve Equation t 43680bo1 [0,-1,0,-142150,20675992] 2 43680bo2 [0,-1,0,-142080,20697300] 2
43680bp (4 curves)	0	2- 3+ 5- 7- 13+	2- 3+ 5- 7- -4 13+  6  4
Curve Equation t 43680bp1 [0,-1,0,-9870,-372600] 4 43680bp2 [0,-1,0,-4800,-759948] 4 43680bp3 [0,-1,0,-15120,72600] 2 43680bp4 [0,-1,0,-157745,-24062175] 2
43680bq (4 curves)	1	2- 3+ 5- 7- 13-	2- 3+ 5- 7-  0 13- -2 -4
Curve Equation t Generators 43680bq1 [0,-1,0,-390,1512] 4 [-6:60:1] 43680bq2 [0,-1,0,1360,9912] 2 [29:270:1] 43680bq3 [0,-1,0,-3120,-65100] 2 [65:50:1] 43680bq4 [0,-1,0,-5265,148737] 4 [-83:84:1]
43680br (4 curves)	1	2- 3+ 5- 7- 13-	2- 3+ 5- 7-  0 13- -2 -4
Curve Equation t Generators 43680br1 [0,-1,0,-40950,-3175848] 4 [244:1140:1] 43680br2 [0,-1,0,-39200,-3461448] 2 [52494:246905:216] 43680br3 [0,-1,0,-42705,-2886975] 4 [-80:105:1] 43680br4 [0,-1,0,-655200,-203912748] 2 [12529:1399350:1]
43680bs (4 curves)	1	2- 3+ 5- 7- 13-	2- 3+ 5- 7-  4 13- -6  4
Curve Equation t Generators 43680bs1 [0,-1,0,-4310,46200] 4 [-38:392:1] 43680bs2 [0,-1,0,15535,335937] 4 [29:900:1] 43680bs3 [0,-1,0,-36160,-2603720] 2 [-103:132:1] 43680bs4 [0,-1,0,-56960,5248020] 4 [157:388:1]
43680bt (4 curves)	1	2- 3+ 5- 7- 13-	2- 3+ 5- 7- -4 13-  2  8
Curve Equation t Generators 43680bt1 [0,-1,0,-1450,11152] 4 [-6:140:1] 43680bt2 [0,-1,0,4920,77400] 2 [85:1050:1] 43680bt3 [0,-1,0,-11200,-445148] 2 [129:490:1] 43680bt4 [0,-1,0,-19825,1080577] 4 [-151:780:1]
43680bu (4 curves)	1	2- 3- 5+ 7+ 13+	2- 3- 5+ 7+  4 13+ -2  4
Curve Equation t Generators 43680bu1 [0,1,0,-1366,18920] 4 [-4:156:1] 43680bu2 [0,1,0,-736,37064] 2 [59:450:1] 43680bu3 [0,1,0,-2016,-1620] 2 [-9:126:1] 43680bu4 [0,1,0,-21841,1235135] 2 [101:264:1]
43680bv (2 curves)	1	2- 3- 5+ 7+ 13+	2- 3- 5+ 7+  4 13+  4 -8
Curve Equation t Generators 43680bv1 [0,1,0,-3568586,-2596166436] 2 [14347305473315200746756:2992595709420998511007170:329150724104588849] 43680bv2 [0,1,0,-57098881,-166088393425] 2 [53558499066349319319123558838742356293:11036145320362124175300743344420551866300:1221474541494487001379436196550189]
43680bw (4 curves)	1	2- 3- 5+ 7+ 13+	2- 3- 5+ 7+ -4 13+  2  0
Curve Equation t Generators 43680bw1 [0,1,0,-1106,11400] 4 [-14:156:1] 43680bw2 [0,1,0,2144,68600] 2 [2:270:1] 43680bw3 [0,1,0,-5201,-135201] 2 [-35:72:1] 43680bw4 [0,1,0,-16856,836700] 2 [79:66:1]
43680bx (2 curves)	0	2- 3- 5+ 7+ 13-	2- 3- 5+ 7+  0 13-  2 -4
Curve Equation t 43680bx1 [0,1,0,34,-36] 2 43680bx2 [0,1,0,-161,-465] 2
43680by (2 curves)	0	2- 3- 5+ 7+ 13-	2- 3- 5+ 7+  6 13-  0 -4
Curve Equation t 43680by1 [0,1,0,-215668726,1218972024344] 2 43680by2 [0,1,0,-207433296,1316357631180] 2
43680bz (2 curves)	1	2- 3- 5+ 7- 13-	2- 3- 5+ 7-  6 13- -4  4
Curve Equation t Generators 43680bz1 [0,1,0,-4646,119304] 2 [22:168:1] 43680bz2 [0,1,0,-1216,294920] 2 [-34:546:1]
43680ca (2 curves)	0	2- 3- 5- 7+ 13+	2- 3- 5- 7+  0 13+  0  0
Curve Equation t 43680ca1 [0,1,0,-178290,-73811412] 2 43680ca2 [0,1,0,-3946145,-3014999025] 2
43680cb (2 curves)	0	2- 3- 5- 7+ 13+	2- 3- 5- 7+ -2 13+  0 -4
Curve Equation t 43680cb1 [0,1,0,-142150,-20675992] 2 43680cb2 [0,1,0,-142080,-20697300] 2
43680cc (4 curves)	0	2- 3- 5- 7+ 13+	2- 3- 5- 7+  4 13+  6 -4
Curve Equation t 43680cc1 [0,1,0,-9870,372600] 4 43680cc2 [0,1,0,-4800,759948] 2 43680cc3 [0,1,0,-15120,-72600] 2 43680cc4 [0,1,0,-157745,24062175] 4
43680cd (4 curves)	1	2- 3- 5- 7+ 13-	2- 3- 5- 7+  0 13-  2 -4
Curve Equation t Generators 43680cd1 [0,1,0,-330,-1800] 4 [-12:24:1] 43680cd2 [0,1,0,840,-10692] 2 [27:180:1] 43680cd3 [0,1,0,-1905,30015] 4 [93:816:1] 43680cd4 [0,1,0,-4880,-132840] 2 [103:684:1]
43680ce (4 curves)	1	2- 3- 5- 7+ 13-	2- 3- 5- 7+  0 13- -2  4
Curve Equation t Generators 43680ce1 [0,1,0,-390,-1512] 4 [36:180:1] 43680ce2 [0,1,0,1360,-9912] 4 [982:30810:1] 43680ce3 [0,1,0,-3120,65100] 2 [730:5925:8] 43680ce4 [0,1,0,-5265,-148737] 2 [101:600:1]
43680cf (4 curves)	1	2- 3- 5- 7+ 13-	2- 3- 5- 7+  0 13- -2  4
Curve Equation t Generators 43680cf1 [0,1,0,-40950,3175848] 4 [126:-180:1] 43680cf2 [0,1,0,-39200,3461448] 4 [-194:1950:1] 43680cf3 [0,1,0,-42705,2886975] 2 [15:-1500:1] 43680cf4 [0,1,0,-655200,203912748] 2 [471:150:1]
43680cg (4 curves)	1	2- 3- 5- 7+ 13-	2- 3- 5- 7+ -4 13-  6 -4
Curve Equation t Generators 43680cg1 [0,1,0,-2730,-55800] 4 [90:660:1] 43680cg2 [0,1,0,-2280,-74340] 2 [714:5313:8] 43680cg3 [0,1,0,-3185,-36417] 4 [-47:108:1] 43680cg4 [0,1,0,-43680,-3528360] 2 [363:5346:1]
43680ch (4 curves)	1	2- 3- 5- 7+ 13-	2- 3- 5- 7+ -4 13- -6 -4
Curve Equation t Generators 43680ch1 [0,1,0,-4310,-46200] 4 [-47:234:1] 43680ch2 [0,1,0,15535,-335937] 4 [31:420:1] 43680ch3 [0,1,0,-36160,2603720] 4 [94:210:1] 43680ch4 [0,1,0,-56960,-5248020] 2 [-137:54:1]
43680ci (2 curves)	1	2- 3- 5- 7+ 13-	2- 3- 5- 7+ -6 13- -2 -2
Curve Equation t Generators 43680ci1 [0,1,0,-195410,33176808] 2 [226:780:1] 43680ci2 [0,1,0,-173440,40945400] 2 [1370:48750:1]
43680cj (4 curves)	1	2- 3- 5- 7- 13+	2- 3- 5- 7-  0 13+  6 -4
Curve Equation t Generators 43680cj1 [0,1,0,-21770,-323400] 4 [-35:630:1] 43680cj2 [0,1,0,83855,-2457025] 4 [50:1365:1] 43680cj3 [0,1,0,-205520,35544600] 2 [315:1470:1] 43680cj4 [0,1,0,-270200,-54083652] 2 [8778:249375:8]
43680ck (2 curves)	1	2- 3- 5- 7- 13+	2- 3- 5- 7-  2 13+ -2 -2
Curve Equation t Generators 43680ck1 [0,1,0,-2099410,-1171528600] 2 [1765:24990:1] 43680ck2 [0,1,0,-2077440,-1197224712] 2 [3386:174930:1]
43680cl (4 curves)	0	2- 3- 5- 7- 13-	2- 3- 5- 7-  0 13-  6 -4
Curve Equation t 43680cl1 [0,1,0,-670,-5800] 4 43680cl2 [0,1,0,1280,-31540] 2 43680cl3 [0,1,0,-3120,60840] 4 43680cl4 [0,1,0,-10225,-401377] 2

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