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	3731a	Isogeny class
Conductor	3731	Conductor
∏ cp	10	Product of Tamagawa factors cp
deg	960	Modular degree for the optimal curve
Δ	-4369004731 = -1 · 7 · 135 · 412	Discriminant
Eigenvalues	0  0  1 7+  0 13-  2  3	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,88,3164]	[a1,a2,a3,a4,a6]
Generators	[14:84:1]	Generators of the group modulo torsion
j	75365351424/4369004731	j-invariant
L	2.9390592895214	L(r)(E,1)/r!
Ω	1.0512428800726	Real period
R	0.2795794716173	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	59696x1 33579b1 93275j1 26117c1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 3731a1

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	0	1	+	0	-	2	3	-1	-3	5	8	-	-9	9	-3	-4	-12	-8	-8	3	1	7	9	1

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Quadratic twists for elliptic curve 3731a1

-4	-3	5	-7	13
59696x1	33579b1	93275j1	26117c1	48503f1

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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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