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	8	Product of Tamagawa factors cp
Δ	7341576489 = 32 · 138	Discriminant
Eigenvalues	-1 3+ -2  4 -4 13+  2  0	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-764,-7324]	[a1,a2,a3,a4,a6]
Generators	[-18:40:1]	Generators of the group modulo torsion
j	10218313/1521	j-invariant
L	1.1623161892614	L(r)(E,1)/r!
Ω	0.91712782597108	Real period
R	2.5346874369027	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	8112bh2 32448be2 1521d2 12675w2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 507c2

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 507c2

-4	8	-3	5	-7	-11	13
8112bh2	32448be2	1521d2	12675w2	24843s2	61347k2	39a1

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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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