Cremona's table of elliptic curves

3757 = 13 · 17²

Field	Data	Notes
Atkin-Lehner	13+ 17+	Signs for the Atkin-Lehner involutions
Class	3757c	Isogeny class
Conductor	3757	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	1541642394461 = 13 · 179	Discriminant
Eigenvalues	-1  2  2  0  0 13+ 17+ -8	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-340737,76413626]	[a1,a2,a3,a4,a6]
Generators	[1868505:2553187057:1]	Generators of the group modulo torsion
j	36892780289/13	j-invariant
L	3.4879978019311	L(r)(E,1)/r!
Ω	0.6845420262373	Real period
R	10.190748466105	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	60112v2 33813g2 93925h2 48841c2	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 3757c2

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
-1	2	2	0	0	+	+	-8	2	-8	4	-10	-2	4	-4	-2	8	-4	-4	0	-10	-2	12	14	-14

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Quadratic twists for elliptic curve 3757c2

-4	-3	5	13	17
60112v2	33813g2	93925h2	48841c2	3757d2

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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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