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	2496c	Isogeny class
Conductor	2496	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	2555904 = 216 · 3 · 13	Discriminant
Eigenvalues	2+ 3+ -2  0  0 13+  2  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-3329,-72831]	[a1,a2,a3,a4,a6]
Generators	[67:20:1]	Generators of the group modulo torsion
j	62275269892/39	j-invariant
L	2.4586088148755	L(r)(E,1)/r!
Ω	0.62850719139244	Real period
R	3.9118228853174	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	2496bb3 312c3 7488n3 62400cq4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2496c3

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	0	0	+	2	4	0	-6	0	2	6	12	-4	-6	8	2	-4	-12	-14	0	-8	-18	-6

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Quadratic twists for elliptic curve 2496c3

-4	8	-3	5	-7	13
2496bb3	312c3	7488n3	62400cq4	122304ed4	32448c4

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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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