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	2496r	Isogeny class
Conductor	2496	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	640	Modular degree for the optimal curve
Δ	2628288 = 26 · 35 · 132	Discriminant
Eigenvalues	2- 3+  0 -2  4 13+ -6  6	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-328,2398]	[a1,a2,a3,a4,a6]
j	61162984000/41067	j-invariant
L	1.2686003950329	L(r)(E,1)/r!
Ω	2.5372007900658	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	2496y1 1248d2 7488bq1 62400he1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2496r1

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

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Quadratic twists for elliptic curve 2496r1

-4	8	-3	5	-7	13
2496y1	1248d2	7488bq1	62400he1	122304hw1	32448bx1

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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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