Cremona's table of elliptic curves

3757 = 13 · 17²

Field	Data	Notes
Atkin-Lehner	13+ 17+	Signs for the Atkin-Lehner involutions
Class	3757b	Isogeny class
Conductor	3757	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	34560	Modular degree for the optimal curve
Δ	1980626399884457 = 136 · 177	Discriminant
Eigenvalues	-1  0 -4  2 -6 13+ 17+  8	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-211747,37495370]	[a1,a2,a3,a4,a6]
Generators	[302:860:1]	Generators of the group modulo torsion
j	43499078731809/82055753	j-invariant
L	1.474400460737	L(r)(E,1)/r!
Ω	0.46688713387887	Real period
R	1.5789688275277	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	60112p1 33813i1 93925f1 48841b1	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 3757b1

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	0	-4	2	-6	+	+	8	-4	6	2	8	0	4	0	-6	0	10	-8	-2	0	0	-4	-2	4

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Quadratic twists for elliptic curve 3757b1

-4	-3	5	13	17
60112p1	33813i1	93925f1	48841b1	221a1

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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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