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	2496o	Isogeny class
Conductor	2496	Conductor
∏ cp	48	Product of Tamagawa factors cp
Δ	59041861632 = 212 · 38 · 133	Discriminant
Eigenvalues	2+ 3- -2 -2 -2 13-  6  2	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-11609,477447]	[a1,a2,a3,a4,a6]
Generators	[34:351:1]	Generators of the group modulo torsion
j	42246001231552/14414517	j-invariant
L	3.2561509498297	L(r)(E,1)/r!
Ω	1.0900261834907	Real period
R	0.24893522430521	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	2496f2 1248f1 7488ba2 62400i2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2496o2

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

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Quadratic twists for elliptic curve 2496o2

-4	8	-3	5	-7	13
2496f2	1248f1	7488ba2	62400i2	122304u2	32448bd2

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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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