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	2576k	Isogeny class
Conductor	2576	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	212344832 = 213 · 72 · 232	Discriminant
Eigenvalues	2- -2 -2 7+ -6 -4 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-224,1012]	[a1,a2,a3,a4,a6]
Generators	[-14:40:1] [-12:46:1]	Generators of the group modulo torsion
j	304821217/51842	j-invariant
L	2.6640663403779	L(r)(E,1)/r!
Ω	1.6953904517093	Real period
R	0.39283964612559	Regulator
r	2	Rank of the group of rational points
S	1.0000000000004	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	322c2 10304s2 23184bq2 64400by2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2576k2

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
-	-2	-2	+	-6	-4	-2	-4	+	-10	8	-8	-2	-6	-12	12	6	-6	2	-16	2	0	-4	-6	2

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Quadratic twists for elliptic curve 2576k2

-4	8	-3	5	-7	-23
322c2	10304s2	23184bq2	64400by2	18032t2	59248bd2

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

Part of Computational Number Theory
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