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	3731c	Isogeny class
Conductor	3731	Conductor
∏ cp	10	Product of Tamagawa factors cp
deg	2720	Modular degree for the optimal curve
Δ	-367283371 = -1 · 75 · 13 · 412	Discriminant
Eigenvalues	-2 -2 -3 7- -2 13+  0 -5	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-112,992]	[a1,a2,a3,a4,a6]
Generators	[-13:20:1] [-7:38:1]	Generators of the group modulo torsion
j	-156765196288/367283371	j-invariant
L	1.6346786909024	L(r)(E,1)/r!
Ω	1.5042418448492	Real period
R	0.10867126828712	Regulator
r	2	Rank of the group of rational points
S	0.99999999999951	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	59696j1 33579g1 93275e1 26117n1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 3731c1

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
-2	-2	-3	-	-2	+	0	-5	-9	-3	1	10	+	3	-7	1	-12	-12	-12	-6	-5	1	-5	-3	-19

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Quadratic twists for elliptic curve 3731c1

-4	-3	5	-7	13
59696j1	33579g1	93275e1	26117n1	48503b1

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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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