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
Δ	-3901614750890649 = -1 · 314 · 138	Discriminant
Eigenvalues	1 3+ -1  2 -2 13+ -7 -6	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-12678,-3060351]	[a1,a2,a3,a4,a6]
Generators	[30720:354243:125]	Generators of the group modulo torsion
j	-276301129/4782969	j-invariant
L	2.0594887788138	L(r)(E,1)/r!
Ω	0.18953883583999	Real period
R	1.8109646409988	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	8112bd2 32448x2 1521e2 12675y2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 507a2

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 507a2

-4	8	-3	5	-7	-11	13
8112bd2	32448x2	1521e2	12675y2	24843q2	61347m2	507b2

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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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