Cremona's table of elliptic curves

123760 = 2⁴ · 5 · 7 · 13 · 17

Class	r	Atkin-Lehner	Eigenvalues
123760a (1 curve)	0	2+ 5+ 7+ 13- 17+	2+  1 5+ 7+ -3 13- 17+  7
Curve Equation t 123760a1 [0,1,0,-91,-416] 1
123760b (4 curves)	1	2+ 5+ 7+ 13- 17-	2+  0 5+ 7+ -4 13- 17-  8
Curve Equation t Generators 123760b1 [0,0,0,142,-453] 2 [147:1788:1] 123760b2 [0,0,0,-703,-4002] 4 [-7:24:1] 123760b3 [0,0,0,-5123,138322] 2 [-3:392:1] 123760b4 [0,0,0,-9803,-373462] 2 [4738:113577:8]
123760c (1 curve)	0	2+ 5+ 7- 13+ 17+	2+  1 5+ 7-  5 13+ 17+  0
Curve Equation t 123760c1 [0,1,0,-11446698856,-503777890922156] 1
123760d (1 curve)	0	2+ 5+ 7- 13+ 17+	2+  2 5+ 7-  1 13+ 17+  4
Curve Equation t 123760d1 [0,-1,0,22084,-398509] 1
123760e (1 curve)	0	2+ 5+ 7- 13+ 17+	2+ -2 5+ 7- -3 13+ 17+  4
Curve Equation t 123760e1 [0,1,0,-44996,-3817541] 1
123760f (4 curves)	0	2+ 5+ 7- 13- 17-	2+  0 5+ 7-  4 13- 17-  4
Curve Equation t 123760f1 [0,0,0,-521498,125237803] 2 123760f2 [0,0,0,-8024623,8749329678] 4 123760f3 [0,0,0,-7706123,9475700778] 2 123760f4 [0,0,0,-128393123,559964838578] 4
123760g (1 curve)	1	2+ 5- 7+ 13+ 17-	2+ -2 5- 7+ -3 13+ 17-  8
Curve Equation t Generators 123760g1 [0,1,0,-120,475] 1 [5:5:1]
123760h (2 curves)	1	2+ 5- 7+ 13- 17+	2+  0 5- 7+ -4 13- 17+ -2
Curve Equation t Generators 123760h1 [0,0,0,218,219] 2 [3:30:1] 123760h2 [0,0,0,-887,1766] 2 [-23:100:1]
123760i (1 curve)	1	2+ 5- 7+ 13- 17+	2+  1 5- 7+ -5 13- 17+  1
Curve Equation t Generators 123760i1 [0,1,0,385,46400] 1 [20:250:1]
123760j (1 curve)	1	2+ 5- 7+ 13- 17+	2+  2 5- 7+ -1 13- 17+  0
Curve Equation t Generators 123760j1 [0,-1,0,-2360,-64885] 1 [1749:6029:27]
123760k (4 curves)	0	2+ 5- 7+ 13- 17-	2+  0 5- 7+  4 13- 17-  0
Curve Equation t 123760k1 [0,0,0,-2642,-39401] 2 123760k2 [0,0,0,-14647,649686] 4 123760k3 [0,0,0,9853,2604786] 4 123760k4 [0,0,0,-231227,42796154] 4
123760l (1 curve)	0	2+ 5- 7+ 13- 17-	2+  1 5- 7+  5 13- 17-  1
Curve Equation t 123760l1 [0,1,0,-30940,-2106212] 1
123760m (1 curve)	0	2+ 5- 7+ 13- 17-	2+ -2 5- 7+ -3 13- 17-  4
Curve Equation t 123760m1 [0,1,0,0,-17] 1
123760n (1 curve)	1	2+ 5- 7- 13+ 17+	2+  1 5- 7-  3 13+ 17+ -3
Curve Equation t Generators 123760n1 [0,1,0,503645,126058600] 1 [120:13720:1]
123760o (1 curve)	1	2+ 5- 7- 13+ 17+	2+ -3 5- 7- -3 13+ 17+ -5
Curve Equation t Generators 123760o1 [0,0,0,-82,-569] 1 [27:130:1]
123760p (2 curves)	0	2+ 5- 7- 13+ 17-	2+  0 5- 7-  4 13+ 17- -2
Curve Equation t 123760p1 [0,0,0,-62,159] 2 123760p2 [0,0,0,113,894] 2
123760q (2 curves)	0	2+ 5- 7- 13- 17+	2+  0 5- 7- -4 13- 17+ -2
Curve Equation t 123760q1 [0,0,0,-2103422,-1174187961] 2 123760q2 [0,0,0,-2094847,-1184236146] 2
123760r (1 curve)	0	2+ 5- 7- 13- 17+	2+  3 5- 7-  3 13- 17+  1
Curve Equation t 123760r1 [0,0,0,233,-18874] 1
123760s (2 curves)	1	2- 5+ 7+ 13- 17+	2-  0 5+ 7+  2 13- 17+  4
Curve Equation t Generators 123760s1 [0,0,0,-304643,61318658] 2 [239:1470:1] 123760s2 [0,0,0,227837,252904962] 2 [-361:11118:1]
123760t (2 curves)	1	2- 5+ 7+ 13- 17+	2-  2 5+ 7+  3 13- 17+ -8
Curve Equation t Generators 123760t1 [0,-1,0,-43706,-3502369] 1 [260635738614879406707110724380817417:9876172859054715481859502897981878809:177515347541943386325741617756349] 123760t2 [0,-1,0,-41046,-3950005] 1 [250416050343:28718249338441:19034163]
123760u (1 curve)	1	2- 5+ 7+ 13- 17+	2- -2 5+ 7+  3 13- 17+  0
Curve Equation t Generators 123760u1 [0,1,0,1014,16939] 1 [467:10127:1]
123760v (1 curve)	2	2- 5+ 7+ 13- 17-	2-  1 5+ 7+ -1 13- 17- -1
Curve Equation t Generators 123760v1 [0,1,0,-10816,6968884] 1 [-156:2210:1]&[-54:2720:1]
123760w (2 curves)	0	2- 5+ 7+ 13- 17-	2- -1 5+ 7+ -3 13- 17- -8
Curve Equation t 123760w1 [0,-1,0,-4993976,-4296251024] 1 123760w2 [0,-1,0,4554584,-17977298320] 1
123760x (4 curves)	0	2- 5+ 7+ 13- 17-	2-  2 5+ 7+  0 13- 17- -8
Curve Equation t 123760x1 [0,-1,0,-21301,-1189524] 2 123760x2 [0,-1,0,-21476,-1168804] 2 123760x3 [0,-1,0,-26741,-529720] 2 123760x4 [0,-1,0,-241116,45260780] 2
123760y (2 curves)	0	2- 5+ 7+ 13- 17-	2-  2 5+ 7+ -3 13- 17-  4
Curve Equation t 123760y1 [0,-1,0,34,-289] 1 123760y2 [0,-1,0,-306,8075] 1
123760z (2 curves)	1	2- 5+ 7- 13+ 17+	2- -2 5+ 7- -2 13+ 17+  6
Curve Equation t Generators 123760z1 [0,1,0,-5216,117364] 2 [12:238:1] 123760z2 [0,1,0,10464,700660] 2 [12:-910:1]
123760ba (2 curves)	1	2- 5+ 7- 13+ 17+	2- -2 5+ 7- -4 13+ 17+  0
Curve Equation t Generators 123760ba1 [0,1,0,-1040508901,12918273942990] 2 [-5074:4250554:1] 123760ba2 [0,1,0,-1051013276,12644113957240] 2 [-54971202:-45090842867:10648]
123760bb (1 curve)	1	2- 5+ 7- 13+ 17+	2- -3 5+ 7- -1 13+ 17+  2
Curve Equation t Generators 123760bb1 [0,0,0,24077,1273522] 1 [151:2890:1]
123760bc (2 curves)	0	2- 5+ 7- 13+ 17-	2-  0 5+ 7-  6 13+ 17-  4
Curve Equation t 123760bc1 [0,0,0,-3988,-79557] 2 123760bc2 [0,0,0,8017,-466118] 2
123760bd (1 curve)	2	2- 5+ 7- 13+ 17-	2- -3 5+ 7-  1 13+ 17- -7
Curve Equation t Generators 123760bd1 [0,0,0,-283,4618] 1 [-1:70:1]&[-19:56:1]
123760be (1 curve)	2	2- 5+ 7- 13- 17+	2- -1 5+ 7-  1 13- 17+ -1
Curve Equation t Generators 123760be1 [0,-1,0,944,36800] 1 [-22:70:1]&[56:512:1]
123760bf (1 curve)	0	2- 5+ 7- 13- 17+	2- -1 5+ 7-  5 13- 17+ -1
Curve Equation t 123760bf1 [0,-1,0,43064,-2718160] 1
123760bg (1 curve)	2	2- 5+ 7- 13- 17+	2- -1 5+ 7- -5 13- 17+ -4
Curve Equation t Generators 123760bg1 [0,-1,0,604064,-230076160] 1 [1568:67600:1]&[736:-24752:1]
123760bh (4 curves)	1	2- 5+ 7- 13- 17-	2-  0 5+ 7-  4 13- 17- -4
Curve Equation t Generators 123760bh1 [0,0,0,-174443,-28040742] 2 [-241:50:1] 123760bh2 [0,0,0,-187963,-23441238] 4 [-243:2808:1] 123760bh3 [0,0,0,462037,-149931238] 4 [1007:36558:1] 123760bh4 [0,0,0,-1054283,397417018] 2 [1423:42174:1]
123760bi (4 curves)	0	2- 5- 7+ 13- 17+	2-  0 5- 7+  4 13- 17+  0
Curve Equation t 123760bi1 [0,0,0,-7307,-225734] 2 123760bi2 [0,0,0,-22987,1069434] 4 123760bi3 [0,0,0,49813,6471194] 2 123760bi4 [0,0,0,-346667,78558426] 4
123760bj (4 curves)	0	2- 5- 7+ 13- 17+	2-  2 5- 7+  0 13- 17+ -2
Curve Equation t 123760bj1 [0,-1,0,-1111825,449640000] 2 123760bj2 [0,-1,0,-523580,923530172] 2 123760bj3 [0,-1,0,-89948825,328383262100] 2 123760bj4 [0,-1,0,-89948580,328385140172] 2
123760bk (1 curve)	1	2- 5- 7+ 13- 17-	2-  1 5- 7+ -1 13- 17- -5
Curve Equation t Generators 123760bk1 [0,1,0,-2129680,-2069286572] 1 [2226:65000:1]
123760bl (1 curve)	1	2- 5- 7+ 13- 17-	2-  1 5- 7+  3 13- 17-  3
Curve Equation t Generators 123760bl1 [0,1,0,-1600040,-973614412] 1 [12206:1340960:1]
123760bm (2 curves)	1	2- 5- 7+ 13- 17-	2- -2 5- 7+  0 13- 17-  0
Curve Equation t Generators 123760bm1 [0,1,0,-85,258] 2 [2:10:1] 123760bm2 [0,1,0,-260,-1352] 2 [-54:95:8]
123760bn (2 curves)	1	2- 5- 7+ 13- 17-	2- -2 5- 7+  2 13- 17- -2
Curve Equation t Generators 123760bn1 [0,1,0,-4457873880,-114559917851372] 2 [5021517:2000441170:27] 123760bn2 [0,1,0,-4261183960,-125127752549100] 2 [723180:612379950:1]
123760bo (2 curves)	0	2- 5- 7- 13+ 17+	2-  2 5- 7- -4 13+ 17+  4
Curve Equation t 123760bo1 [0,-1,0,-365,1100] 2 123760bo2 [0,-1,0,-4740,127100] 2
123760bp (1 curve)	1	2- 5- 7- 13+ 17-	2-  1 5- 7-  5 13+ 17-  0
Curve Equation t Generators 123760bp1 [0,1,0,-1160,-23692] 1 [116:1190:1]
123760bq (1 curve)	1	2- 5- 7- 13+ 17-	2- -2 5- 7- -1 13+ 17-  0
Curve Equation t Generators 123760bq1 [0,1,0,-4590,1680535] 1 [323:5831:1]
123760br (1 curve)	1	2- 5- 7- 13- 17+	2- -1 5- 7- -3 13- 17+  3
Curve Equation t Generators 123760br1 [0,-1,0,-9560,362992] 1 [44:160:1]
123760bs (2 curves)	1	2- 5- 7- 13- 17+	2-  2 5- 7-  0 13- 17+  6
Curve Equation t Generators 123760bs1 [0,-1,0,-1825,-29400] 2 [101100:425645:1728] 123760bs2 [0,-1,0,-1580,-37828] 2 [1562:21255:8]
123760bt (2 curves)	1	2- 5- 7- 13- 17+	2-  2 5- 7-  2 13- 17+  2
Curve Equation t Generators 123760bt1 [0,-1,0,-156280,23831472] 2 [5988:4760:27] 123760bt2 [0,-1,0,-152360,25079600] 2 [130:2730:1]
123760bu (2 curves)	1	2- 5- 7- 13- 17+	2- -2 5- 7- -2 13- 17+ -2
Curve Equation t Generators 123760bu1 [0,1,0,-27653787400,1712696086897140] 2 [-147842:50692096:1] 123760bu2 [0,1,0,10897436920,6113256661066228] 2 [-114228:58120790:1]
123760bv (4 curves)	0	2- 5- 7- 13- 17-	2-  0 5- 7-  0 13- 17-  0
Curve Equation t 123760bv1 [0,0,0,-20626667,-28808390886] 2 123760bv2 [0,0,0,-104512747,385874056986] 4 123760bv3 [0,0,0,92177173,1669354460954] 4 123760bv4 [0,0,0,-1643379947,25642070316826] 4
123760bw (4 curves)	0	2- 5- 7- 13- 17-	2-  0 5- 7- -4 13- 17-  4
Curve Equation t 123760bw1 [0,0,0,1213,67394] 2 123760bw2 [0,0,0,-19267,956226] 4 123760bw3 [0,0,0,-64067,-5127614] 2 123760bw4 [0,0,0,-302147,63925314] 4
123760bx (1 curve)	0	2- 5- 7- 13- 17-	2-  2 5- 7- -1 13- 17- -4
Curve Equation t 123760bx1 [0,-1,0,-58570,-5437725] 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