Cremona's table of elliptic curves

504 = 2³ · 3² · 7

Field	Data	Notes
Atkin-Lehner	2+ 3+ 7+	Signs for the Atkin-Lehner involutions
Class	504a	Isogeny class
Conductor	504	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	32	Modular degree for the optimal curve
Δ	-21168 = -1 · 24 · 33 · 72	Discriminant
Eigenvalues	2+ 3+ -2 7+ -2  2 -6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-6,9]	[a1,a2,a3,a4,a6]
Generators	[0:3:1]	Generators of the group modulo torsion
j	-55296/49	j-invariant
L	1.8034162570636	L(r)(E,1)/r!
Ω	3.500939456238	Real period
R	0.25756176015131	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	1008d1 4032a1 504d1 12600bl1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 504a1

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
+	+	-2	+	-2	2	-6	-4	-6	0	-4	10	-2	-4	-4	12	-12	6	-4	14	-2	-8	16	6	-18

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Quadratic twists for elliptic curve 504a1

-4	8	-3	5	-7	-11	13
1008d1	4032a1	504d1	12600bl1	3528d1	60984bt1	85176bn1

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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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