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	4	Product of Tamagawa factors cp
Δ	3144241152 = 212 · 310 · 13	Discriminant
Eigenvalues	2- 3+  0 -2  4 13+ -6  6	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-393,1449]	[a1,a2,a3,a4,a6]
j	1643032000/767637	j-invariant
L	1.2686003950329	L(r)(E,1)/r!
Ω	1.2686003950329	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	2496y2 1248d1 7488bq2 62400he2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2496r2

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 2496r2

-4	8	-3	5	-7	13
2496y2	1248d1	7488bq2	62400he2	122304hw2	32448bx2

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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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