Cremona's table of elliptic curves

3731 = 7 · 13 · 41

Field	Data	Notes
Atkin-Lehner	7+ 13- 41-	Signs for the Atkin-Lehner involutions
Class	3731b	Isogeny class
Conductor	3731	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	4200	Modular degree for the optimal curve
Δ	-8958131 = -1 · 75 · 13 · 41	Discriminant
Eigenvalues	0 -3  1 7+  0 13- -7  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,-7192,234759]	[a1,a2,a3,a4,a6]
Generators	[49:0:1]	Generators of the group modulo torsion
j	-41140801499037696/8958131	j-invariant
L	1.6832117667294	L(r)(E,1)/r!
Ω	1.8356609674335	Real period
R	0.91695133066034	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	59696y1 33579c1 93275l1 26117d1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 3731b1

a2	a3	a5	a7	a11	a13	a17	a19	a23	a29	a31	a37	a41	a43	a47	a53	a59	a61	a67	a71	a73	a79	a83	a89	a97
0	-3	1	+	0	-	-7	0	-1	0	-4	8	-	12	6	0	11	0	7	16	-9	-14	7	6	-2

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Quadratic twists for elliptic curve 3731b1

-4	-3	5	-7	13
59696y1	33579c1	93275l1	26117d1	48503g1

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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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