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	2496b	Isogeny class
Conductor	2496	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	-226385362944 = -1 · 215 · 312 · 13	Discriminant
Eigenvalues	2+ 3+  2  0  4 13+ -6 -8	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-417,23265]	[a1,a2,a3,a4,a6]
Generators	[67:540:1]	Generators of the group modulo torsion
j	-245314376/6908733	j-invariant
L	3.1154670108105	L(r)(E,1)/r!
Ω	0.83103499402351	Real period
R	3.7488999057991	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	2496h4 1248e4 7488r4 62400cr3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2496b4

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

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Quadratic twists for elliptic curve 2496b4

-4	8	-3	5	-7	13
2496h4	1248e4	7488r4	62400cr3	122304eh3	32448f3

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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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