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	2496v	Isogeny class
Conductor	2496	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	384	Modular degree for the optimal curve
Δ	119808 = 210 · 32 · 13	Discriminant
Eigenvalues	2- 3+  4  2 -4 13+  2 -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-21,-27]	[a1,a2,a3,a4,a6]
j	1048576/117	j-invariant
L	2.2375499551425	L(r)(E,1)/r!
Ω	2.2375499551425	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	2496l1 624j1 7488bw1 62400hg1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2496v1

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
-	+	4	2	-4	+	2	-2	0	6	10	-10	8	4	4	10	-8	14	2	-16	-10	16	0	-4	-2

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Quadratic twists for elliptic curve 2496v1

-4	8	-3	5	-7	13
2496l1	624j1	7488bw1	62400hg1	122304it1	32448cr1

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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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