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	2496m	Isogeny class
Conductor	2496	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	-8306688 = -1 · 214 · 3 · 132	Discriminant
Eigenvalues	2+ 3-  0 -4  2 13- -6  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,47,-49]	[a1,a2,a3,a4,a6]
Generators	[10:39:1]	Generators of the group modulo torsion
j	686000/507	j-invariant
L	3.4900171241411	L(r)(E,1)/r!
Ω	1.3045679220114	Real period
R	2.6752283765801	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	2496w2 312b2 7488w2 62400s2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2496m2

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

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Quadratic twists for elliptic curve 2496m2

-4	8	-3	5	-7	13
2496w2	312b2	7488w2	62400s2	122304j2	32448w2

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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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