Cremona's table of elliptic curves

507 = 3 · 13²

Field	Data	Notes
Atkin-Lehner	3+ 13+	Signs for the Atkin-Lehner involutions
Class	507c	Isogeny class
Conductor	507	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	413575475547 = 3 · 1310	Discriminant
Eigenvalues	-1 3+ -2  4 -4 13+  2  0	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-3299,64670]	[a1,a2,a3,a4,a6]
Generators	[44:62:1]	Generators of the group modulo torsion
j	822656953/85683	j-invariant
L	1.1623161892614	L(r)(E,1)/r!
Ω	0.91712782597108	Real period
R	1.2673437184513	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	8112bh3 32448be3 1521d3 12675w4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 507c4

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	4	-4	+	2	0	0	-10	-4	2	-6	-12	0	6	-12	-2	8	0	-2	8	-4	2	-10

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Quadratic twists for elliptic curve 507c4

-4	8	-3	5	-7	-11	13
8112bh3	32448be3	1521d3	12675w4	24843s3	61347k3	39a3

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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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