Cremona's table of elliptic curves

2496 = 2⁶ · 3 · 13

Field	Data	Notes
Atkin-Lehner	2+ 3+ 13+	Signs for the Atkin-Lehner involutions
Class	2496a	Isogeny class
Conductor	2496	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	384	Modular degree for the optimal curve
Δ	9704448 = 210 · 36 · 13	Discriminant
Eigenvalues	2+ 3+  0  2  0 13+ -6 -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-53,21]	[a1,a2,a3,a4,a6]
Generators	[-3:12:1]	Generators of the group modulo torsion
j	16384000/9477	j-invariant
L	2.8807792798504	L(r)(E,1)/r!
Ω	1.9461694191795	Real period
R	1.4802304729795	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	2496ba1 156b1 7488k1 62400cz1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2496a1

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

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Quadratic twists for elliptic curve 2496a1

-4	8	-3	5	-7	13
2496ba1	156b1	7488k1	62400cz1	122304dz1	32448b1

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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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