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	2496k	Isogeny class
Conductor	2496	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	512	Modular degree for the optimal curve
Δ	-10223616 = -1 · 218 · 3 · 13	Discriminant
Eigenvalues	2+ 3- -2 -4 -4 13+  2  0	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,31,-129]	[a1,a2,a3,a4,a6]
j	12167/39	j-invariant
L	1.1691131702714	L(r)(E,1)/r!
Ω	1.1691131702714	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	2496t1 39a4 7488p1 62400bf1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2496k1

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

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Quadratic twists for elliptic curve 2496k1

-4	8	-3	5	-7	13
2496t1	39a4	7488p1	62400bf1	122304bz1	32448be1

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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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