Cremona's table of elliptic curves

78585 = 3 · 5 · 13² · 31

Class	r	Atkin-Lehner	Eigenvalues
78585a (2 curves)	1	3+ 5+ 13+ 31+	-1 3+ 5+  2  4 13+  2  8
Curve Equation t Generators 78585a1 [1,1,1,-1271,41348] 2 [74:562:1] 78585a2 [1,1,1,-27466,1738784] 2 [86:105:1]
78585b (2 curves)	1	3+ 5+ 13+ 31+	-1 3+ 5+ -2  2 13+  7 -1
Curve Equation t Generators 78585b1 [1,1,1,-193672736,-2692565783692] 1 [1228152423616741013975801577742181642194275854264418:882341574562413200503157037997250019257220097958140288:2374417703013679594715437281970901346737114701] 78585b2 [1,1,1,-648277749961,-200904827131421782] 1 [288307536703305092538268802737967677497755617158334197004457901869110668084367363401015088291765178169975526004100413641033880910860831001379057529112570513126810930665783233522931531199781737494810736186259906743703055616304212550249099736428422518678896447374211783071290245210938073466868337698810673433032088785305101886366396181318671599532894211369131588841767841685416:-36538822157410434882711291565399093383789265730672196257592591303468648406791777379480078321241182146378029636561737707260335574755338344785871214875041920957323038971689357845025986339619293102279705680696901081257751033206376411774675698652086480248925412369039600062432153822219883577573278637270136051222016963279239307273309578675083740617798147703946010282873271361539974:307746928811417750051524432512039735469291781738546068550835940875184669724168557633967023121277185618953134080428022433018484889195508846854583699027752328994103383913180160470306475754574466602300773227360706735400367523368787726031692093828676407576724572679699118091299880769623136333796106805337653010877428807953600251613035125874830382218552354589262056919969747]
78585c (1 curve)	1	3+ 5+ 13+ 31+	2 3+ 5+ -2  5 13+  4  2
Curve Equation t Generators 78585c1 [0,-1,1,1634,156561] 1 [1034:12671:8]
78585d (1 curve)	0	3+ 5- 13+ 31+	0 3+ 5-  3  3 13+ -1 -6
Curve Equation t 78585d1 [0,-1,1,-16836625225,-840971078947842] 1
78585e (4 curves)	0	3+ 5- 13+ 31+	-1 3+ 5- -4  4 13+ -6 -4
Curve Equation t 78585e1 [1,1,1,-5665,133622] 4 78585e2 [1,1,1,-26790,-1573278] 4 78585e3 [1,1,1,28135,-7131688] 2 78585e4 [1,1,1,-419715,-104833968] 2
78585f (1 curve)	0	3+ 5- 13+ 31+	2 3+ 5-  5 -2 13+  6 -4
Curve Equation t 78585f1 [0,-1,1,-1091120,-407412289] 1
78585g (2 curves)	1	3+ 5- 13+ 31-	1 3+ 5-  2 -2 13+  7  1
Curve Equation t Generators 78585g1 [1,1,0,-1145992,-1226005529] 1 [2242:85369:1] 78585g2 [1,1,0,-3835963017,-91446549167124] 1 [144540:48649716:1]
78585h (1 curve)	0	3- 5+ 13+ 31+	2 3- 5+  3  2 13+  2  4
Curve Equation t 78585h1 [0,1,1,-11886,-338659] 1
78585i (1 curve)	1	3- 5+ 13+ 31-	1 3- 5+  0  4 13+  5 -1
Curve Equation t Generators 78585i1 [1,0,1,-4,-1519] 1 [79:662:1]
78585j (4 curves)	1	3- 5+ 13+ 31-	1 3- 5+  4  4 13+ -6  4
Curve Equation t Generators 78585j1 [1,0,1,-1694,-26869] 2 [-1572069975:1144601788:63521199] 78585j2 [1,0,1,-2539,2537] 4 [165684:8346001:64] 78585j3 [1,0,1,10136,22817] 2 [56808108:-2920613555:21952] 78585j4 [1,0,1,-28734,1867621] 2 [65:492:1]
78585k (1 curve)	1	3- 5+ 13+ 31-	-2 3- 5+ -2 -5 13+  0 -2
Curve Equation t Generators 78585k1 [0,1,1,3195734,-49656262574] 1 [28877:4911562:1]
78585l (2 curves)	1	3- 5+ 13- 31+	1 3- 5+  0  0 13-  6  4
Curve Equation t Generators 78585l1 [1,0,1,-12679,1752701] 2 [147:34949:27] 78585l2 [1,0,1,-309274,66054497] 2 [-39:8854:1]
78585m (1 curve)	1	3- 5+ 13- 31+	1 3- 5+  0  3 13-  0  1
Curve Equation t Generators 78585m1 [1,0,1,-9754,-372019] 1 [4863:49646:27]
78585n (1 curve)	0	3- 5+ 13- 31-	2 3- 5+  1  1 13- -5  4
Curve Equation t 78585n1 [0,1,1,-2927136,2272035341] 1
78585o (3 curves)	1	3- 5- 13+ 31+	0 3- 5-  1  3 13+ -3 -2
Curve Equation t Generators 78585o1 [0,1,1,-637760595,6198972986756] 1 [14550:6277:1] 78585o2 [0,1,1,-635114055,6252973951709] 1 [36351:5585812:1] 78585o3 [0,1,1,2468521935,29859273629306] 1 [12401730:6387694948:729]
78585p (3 curves)	1	3- 5- 13+ 31+	0 3- 5-  1 -6 13+  6 -2
Curve Equation t Generators 78585p1 [0,1,1,-103315,12730111] 1 [173:253:1] 78585p2 [0,1,1,-422725,-93537596] 1 [-412:3295:1] 78585p3 [0,1,1,-33114085,-73355488319] 1 [-89709:71:27]
78585q (4 curves)	1	3- 5- 13+ 31+	-1 3- 5-  0 -4 13+  2  4
Curve Equation t Generators 78585q1 [1,0,0,-3149065,2566624592] 4 [-571:64928:1] 78585q2 [1,0,0,-53045470,148693236275] 4 [-2365:511985:1] 78585q3 [1,0,0,-55714825,132899730482] 2 [-6421:478523:1] 78585q4 [1,0,0,-848718595,9516789475400] 2 [16820:-8350:1]
78585r (1 curve)	1	3- 5- 13+ 31+	-1 3- 5-  0 -4 13+  5  1
Curve Equation t Generators 78585r1 [1,0,0,-595,-3336100] 1 [245:3230:1]
78585s (1 curve)	1	3- 5- 13+ 31+	-2 3- 5- -2  1 13+ -4  6
Curve Equation t Generators 78585s1 [0,1,1,-13623677500,-616176057131696] 1 [1359401:1578923482:1]
78585t (1 curve)	0	3- 5- 13+ 31-	0 3- 5-  5 -1 13+  5  6
Curve Equation t 78585t1 [0,1,1,-612005,-393975994] 1
78585u (4 curves)	0	3- 5- 13+ 31-	-1 3- 5-  0  0 13+ -2 -4
Curve Equation t 78585u1 [1,0,0,-39465,1953600] 2 78585u2 [1,0,0,-567590,164510475] 4 78585u3 [1,0,0,-504215,202674900] 2 78585u4 [1,0,0,-9080965,10532098550] 2
78585v (1 curve)	2	3- 5- 13- 31+	-2 3- 5- -1 -1 13- -5 -4
Curve Equation t Generators 78585v1 [0,1,1,-17320,1028824] 1 [-139:877:1]&[-112:1255:1]
78585w (2 curves)	1	3- 5- 13- 31-	-1 3- 5-  0  0 13-  6 -4
Curve Equation t Generators 78585w1 [1,0,0,-75,792] 2 [-3:33:1] 78585w2 [1,0,0,-1830,29925] 2 [-15:240:1]
78585x (1 curve)	1	3- 5- 13- 31-	-1 3- 5-  0 -3 13-  0 -1
Curve Equation t Generators 78585x1 [1,0,0,-1648345,-815676850] 1 [1535:15710:1]

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