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	504g	Isogeny class
Conductor	504	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	141087744 = 210 · 39 · 7	Discriminant
Eigenvalues	2- 3- -2 7-  0  6  2  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-36291,-2661010]	[a1,a2,a3,a4,a6]
j	7080974546692/189	j-invariant
L	1.3835976409306	L(r)(E,1)/r!
Ω	0.34589941023264	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	4	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	1008e4 4032o3 168b4 12600m3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 504g3

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

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Quadratic twists for elliptic curve 504g3

-4	8	-3	5	-7	-11	13
1008e4	4032o3	168b4	12600m3	3528y4	60984z4	85176o4

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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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