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	4	Product of Tamagawa factors cp
Δ	20247552 = 210 · 32 · 133	Discriminant
Eigenvalues	2+ 3+  0  2  0 13+ -6 -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-2933,-60171]	[a1,a2,a3,a4,a6]
Generators	[116:1071:1]	Generators of the group modulo torsion
j	2725888000000/19773	j-invariant
L	2.8807792798504	L(r)(E,1)/r!
Ω	0.6487231397265	Real period
R	4.4406914189386	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	2496ba3 156b3 7488k3 62400cz3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2496a3

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 2496a3

-4	8	-3	5	-7	13
2496ba3	156b3	7488k3	62400cz3	122304dz3	32448b3

---

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