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	2496b	Isogeny class
Conductor	2496	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	768	Modular degree for the optimal curve
Δ	49353408 = 26 · 33 · 134	Discriminant
Eigenvalues	2+ 3+  2  0  4 13+ -6 -8	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-92,-18]	[a1,a2,a3,a4,a6]
Generators	[-22:115:8]	Generators of the group modulo torsion
j	1360251712/771147	j-invariant
L	3.1154670108105	L(r)(E,1)/r!
Ω	1.662069988047	Real period
R	3.7488999057991	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	2496h1 1248e2 7488r1 62400cr1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2496b1

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

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Quadratic twists for elliptic curve 2496b1

-4	8	-3	5	-7	13
2496h1	1248e2	7488r1	62400cr1	122304eh1	32448f1

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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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