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	2496u	Isogeny class
Conductor	2496	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	669698211446784 = 226 · 310 · 132	Discriminant
Eigenvalues	2- 3+ -2 -4 -4 13+  2 -8	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-83169,-9119871]	[a1,a2,a3,a4,a6]
j	242702053576633/2554695936	j-invariant
L	0.28130981183044	L(r)(E,1)/r!
Ω	0.28130981183044	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	2496j2 624i2 7488bt2 62400hn2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2496u2

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	-8	0	-6	4	2	-10	4	-8	10	4	2	-16	8	2	-8	12	14	10

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Quadratic twists for elliptic curve 2496u2

-4	8	-3	5	-7	13
2496j2	624i2	7488bt2	62400hn2	122304ij2	32448cg2

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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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