Cremona's table of elliptic curves

5746 = 2 · 13² · 17

Class	r	Atkin-Lehner	Eigenvalues
5746a (2 curves)	1	2+ 13+ 17+	2+  0 -2 -4  2 13+ 17+  0
Curve Equation t Generators 5746a1 [1,-1,0,-15833,746201] 2 [-107:1152:1] 5746a2 [1,-1,0,6137,2640015] 2 [-81:1308:1]
5746b (1 curve)	1	2+ 13+ 17+	2+ -1 -4  1 -4 13+ 17+ -2
Curve Equation t Generators 5746b1 [1,1,0,23,5] 1 [2:7:1]
5746c (2 curves)	1	2+ 13+ 17+	2+  2  2 -2 -4 13+ 17+  4
Curve Equation t Generators 5746c1 [1,1,0,-1524,-20548] 2 [-762:1226:27] 5746c2 [1,1,0,-23494,-1395870] 2 [867:24684:1]
5746d (2 curves)	1	2+ 13+ 17+	2+  2 -4  4  2 13+ 17+  4
Curve Equation t Generators 5746d1 [1,1,0,-24496722,16644233780] 2 [-18110232620883489:709852588420302500:3931594053687] 5746d2 [1,1,0,-316961362,2170061378100] 2 [212922680856438569593049828607:-60871979686167461452017659154908:2508573285321012576270423]
5746e (4 curves)	1	2+ 13+ 17+	2+ -2  0  4 -6 13+ 17+  4
Curve Equation t Generators 5746e1 [1,0,1,-511,2706] 2 [-12:90:1] 5746e2 [1,0,1,-7271,237954] 2 [54:32:1] 5746e3 [1,0,1,-17411,-885558] 2 [157:428:1] 5746e4 [1,0,1,-19101,-703714] 2 [11208:1180885:1]
5746f (1 curve)	1	2+ 13+ 17+	2+ -3  4 -1 -4 13+ 17+ -6
Curve Equation t Generators 5746f1 [1,-1,0,-719380,-234720992] 1 [6843804:480136148:1331]
5746g (2 curves)	0	2+ 13+ 17-	2+  0  4  2  2 13+ 17-  0
Curve Equation t 5746g1 [1,-1,0,-29015,-1108067] 2 5746g2 [1,-1,0,-204775,34922733] 2
5746h (1 curve)	0	2- 13+ 17+	2- -1  4 -1  4 13+ 17+  2
Curve Equation t 5746h1 [1,1,1,3799,-8169] 1
5746i (1 curve)	0	2- 13+ 17+	2- -3 -4  1  4 13+ 17+  6
Curve Equation t 5746i1 [1,-1,1,-4257,-105855] 1
5746j (2 curves)	1	2- 13+ 17-	2-  2 -2 -2 -2 13+ 17-  4
Curve Equation t Generators 5746j1 [1,1,1,-9214,-331973] 2 [889:25919:1] 5746j2 [1,1,1,4306,-1208069] 2 [131:1209:1]

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