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	237247315968 = 214 · 3 · 136	Discriminant
Eigenvalues	2+ 3+  0  2  0 13+ -6 -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-2993,-57519]	[a1,a2,a3,a4,a6]
Generators	[-35:56:1]	Generators of the group modulo torsion
j	181037698000/14480427	j-invariant
L	2.8807792798504	L(r)(E,1)/r!
Ω	0.6487231397265	Real period
R	2.2203457094693	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	2496ba4 156b4 7488k4 62400cz4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2496a4

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 2496a4

-4	8	-3	5	-7	13
2496ba4	156b4	7488k4	62400cz4	122304dz4	32448b4

---

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