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	504b	Isogeny class
Conductor	504	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	96	Modular degree for the optimal curve
Δ	2204496 = 24 · 39 · 7	Discriminant
Eigenvalues	2+ 3+  2 7-  6 -6 -2  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-54,-135]	[a1,a2,a3,a4,a6]
j	55296/7	j-invariant
L	1.7758299334867	L(r)(E,1)/r!
Ω	1.7758299334867	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	1008a1 4032d1 504e1 12600bj1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 504b1

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

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Quadratic twists for elliptic curve 504b1

-4	8	-3	5	-7	-11	13
1008a1	4032d1	504e1	12600bj1	3528e1	60984bp1	85176bh1

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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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