Cremona's table of elliptic curves

3757 = 13 · 17²

Field	Data	Notes
Atkin-Lehner	13+ 17+	Signs for the Atkin-Lehner involutions
Class	3757d	Isogeny class
Conductor	3757	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	512	Modular degree for the optimal curve
Δ	830297 = 132 · 173	Discriminant
Eigenvalues	-1 -2 -2  0  0 13+ 17+ -8	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-74,235]	[a1,a2,a3,a4,a6]
Generators	[3:5:1]	Generators of the group modulo torsion
j	9129329/169	j-invariant
L	1.1132329673153	L(r)(E,1)/r!
Ω	2.8224390793507	Real period
R	0.39442231914226	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	60112r1 33813f1 93925g1 48841d1	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 3757d1

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 3757d1

-4	-3	5	13	17
60112r1	33813f1	93925g1	48841d1	3757c1

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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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