Cremona's table of elliptic curves

2576 = 2⁴ · 7 · 23

Field	Data	Notes
Atkin-Lehner	2+ 7- 23-	Signs for the Atkin-Lehner involutions
Class	2576i	Isogeny class
Conductor	2576	Conductor
∏ cp	24	Product of Tamagawa factors cp
deg	5376	Modular degree for the optimal curve
Δ	-1122245340272 = -1 · 24 · 78 · 233	Discriminant
Eigenvalues	2+ -3  2 7- -2 -1  0 -2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-8419,-301667]	[a1,a2,a3,a4,a6]
Generators	[404:7889:1]	Generators of the group modulo torsion
j	-4124632486295808/70140333767	j-invariant
L	2.3064785995149	L(r)(E,1)/r!
Ω	0.24895222323396	Real period
R	0.38603099715832	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	1288g1 10304bl1 23184m1 64400f1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2576i1

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
+	-3	2	-	-2	-1	0	-2	-	-3	1	-2	-1	-8	5	-6	0	6	10	-7	13	2	4	-12	-12

---

Quadratic twists for elliptic curve 2576i1

-4	8	-3	5	-7	-23
1288g1	10304bl1	23184m1	64400f1	18032o1	59248i1

---

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