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	2496m	Isogeny class
Conductor	2496	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	256	Modular degree for the optimal curve
Δ	119808 = 210 · 32 · 13	Discriminant
Eigenvalues	2+ 3-  0 -4  2 13- -6  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-13,-13]	[a1,a2,a3,a4,a6]
Generators	[-2:3:1]	Generators of the group modulo torsion
j	256000/117	j-invariant
L	3.4900171241411	L(r)(E,1)/r!
Ω	2.6091358440228	Real period
R	1.3376141882901	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	2496w1 312b1 7488w1 62400s1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2496m1

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

---

Quadratic twists for elliptic curve 2496m1

-4	8	-3	5	-7	13
2496w1	312b1	7488w1	62400s1	122304j1	32448w1

---

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