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	504h	Isogeny class
Conductor	504	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	73156608 = 211 · 36 · 72	Discriminant
Eigenvalues	2- 3-  4 7-  0  0  2 -2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-363,2630]	[a1,a2,a3,a4,a6]
j	3543122/49	j-invariant
L	1.9475249697668	L(r)(E,1)/r!
Ω	1.9475249697668	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	1008f2 4032p2 56b2 12600k2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 504h2

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
-	-	4	-	0	0	2	-2	-8	-2	4	-6	2	8	4	10	-6	4	-12	0	-14	-8	-6	-10	-2

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Quadratic twists for elliptic curve 504h2

-4	8	-3	5	-7	-11	13
1008f2	4032p2	56b2	12600k2	3528ba2	60984bc2	85176y2

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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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