Cremona's table of elliptic curves

507 = 3 · 13²

Field	Data	Notes
Atkin-Lehner	3+ 13+	Signs for the Atkin-Lehner involutions
Class	507a	Isogeny class
Conductor	507	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	312	Modular degree for the optimal curve
Δ	-7341576489 = -1 · 32 · 138	Discriminant
Eigenvalues	1 3+ -1  2 -2 13+ -7 -6	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-1693,26434]	[a1,a2,a3,a4,a6]
Generators	[70:472:1]	Generators of the group modulo torsion
j	-658489/9	j-invariant
L	2.0594887788138	L(r)(E,1)/r!
Ω	1.3267718508799	Real period
R	0.25870923442841	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	8112bd1 32448x1 1521e1 12675y1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 507a1

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	+	-1	2	-2	+	-7	-6	-6	-1	4	1	9	6	6	-9	0	1	-2	6	11	-4	-14	-14	-2

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Quadratic twists for elliptic curve 507a1

-4	8	-3	5	-7	-11	13
8112bd1	32448x1	1521e1	12675y1	24843q1	61347m1	507b1

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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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