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	2496a	Isogeny class
Conductor	2496	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	74760192 = 214 · 33 · 132	Discriminant
Eigenvalues	2+ 3+  0  2  0 13+ -6 -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-593,5745]	[a1,a2,a3,a4,a6]
Generators	[-11:104:1]	Generators of the group modulo torsion
j	1409938000/4563	j-invariant
L	2.8807792798504	L(r)(E,1)/r!
Ω	1.9461694191795	Real period
R	0.74011523648977	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	2496ba2 156b2 7488k2 62400cz2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2496a2

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

---

Quadratic twists for elliptic curve 2496a2

-4	8	-3	5	-7	13
2496ba2	156b2	7488k2	62400cz2	122304dz2	32448b2

---

Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
Back to Tables and computations