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	2496h	Isogeny class
Conductor	2496	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	768	Modular degree for the optimal curve
Δ	49353408 = 26 · 33 · 134	Discriminant
Eigenvalues	2+ 3-  2  0 -4 13+ -6  8	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-92,18]	[a1,a2,a3,a4,a6]
j	1360251712/771147	j-invariant
L	2.58935849267	L(r)(E,1)/r!
Ω	1.7262389951133	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	2496b1 1248h3 7488q1 62400ba1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2496h1

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 2496h1

-4	8	-3	5	-7	13
2496b1	1248h3	7488q1	62400ba1	122304cd1	32448bi1

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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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