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	2496ba	Isogeny class
Conductor	2496	Conductor
∏ cp	12	Product of Tamagawa factors cp
Δ	74760192 = 214 · 33 · 132	Discriminant
Eigenvalues	2- 3-  0 -2  0 13+ -6  2	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-593,-5745]	[a1,a2,a3,a4,a6]
Generators	[-14:3:1]	Generators of the group modulo torsion
j	1409938000/4563	j-invariant
L	3.5741520120113	L(r)(E,1)/r!
Ω	0.96751870915259	Real period
R	1.2313808433195	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	2496a2 624g2 7488bp2 62400ex2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2496ba2

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

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Quadratic twists for elliptic curve 2496ba2

-4	8	-3	5	-7	13
2496a2	624g2	7488bp2	62400ex2	122304fw2	32448cy2

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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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