Cremona's table of elliptic curves

3757 = 13 · 17²

Field	Data	Notes
Atkin-Lehner	13+ 17+	Signs for the Atkin-Lehner involutions
Class	3757a	Isogeny class
Conductor	3757	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-199234608272401 = -1 · 134 · 178	Discriminant
Eigenvalues	1 -2 -2 -2  6 13+ 17+  4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-15757,1018845]	[a1,a2,a3,a4,a6]
Generators	[1110:9267:8]	Generators of the group modulo torsion
j	-17923019113/8254129	j-invariant
L	2.4046925971221	L(r)(E,1)/r!
Ω	0.52778179211763	Real period
R	2.2781125012609	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	60112t2 33813k2 93925j2 48841e2	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 3757a2

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	-2	6	+	+	4	-6	6	2	-2	6	0	-4	14	4	-2	0	10	-10	-14	12	-18	-2

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Quadratic twists for elliptic curve 3757a2

-4	-3	5	13	17
60112t2	33813k2	93925j2	48841e2	221b2

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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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