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
deg	6912	Modular degree for the optimal curve
Δ	69347235737 = 132 · 177	Discriminant
Eigenvalues	1 -2 -2 -2  6 13+ 17+  4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-17202,866831]	[a1,a2,a3,a4,a6]
Generators	[143:1084:1]	Generators of the group modulo torsion
j	23320116793/2873	j-invariant
L	2.4046925971221	L(r)(E,1)/r!
Ω	1.0555635842353	Real period
R	1.1390562506304	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	60112t1 33813k1 93925j1 48841e1	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 3757a1

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 3757a1

-4	-3	5	13	17
60112t1	33813k1	93925j1	48841e1	221b1

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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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