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	2496x	Isogeny class
Conductor	2496	Conductor
∏ cp	12	Product of Tamagawa factors cp
Δ	-19217032593408 = -1 · 214 · 35 · 136	Discriminant
Eigenvalues	2- 3+ -4  0 -2 13-  2  8	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,2255,-207599]	[a1,a2,a3,a4,a6]
Generators	[99:988:1]	Generators of the group modulo torsion
j	77366117936/1172914587	j-invariant
L	2.1343964162927	L(r)(E,1)/r!
Ω	0.33554836909749	Real period
R	2.120306750443	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	2496p2 624e2 7488cc2 62400gd2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2496x2

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

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Quadratic twists for elliptic curve 2496x2

-4	8	-3	5	-7	13
2496p2	624e2	7488cc2	62400gd2	122304ht2	32448cq2

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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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