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	2576n	Isogeny class
Conductor	2576	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	2688	Modular degree for the optimal curve
Δ	-248504123392 = -1 · 226 · 7 · 232	Discriminant
Eigenvalues	2- -2  0 7+ -4  0  6  6	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,552,-23276]	[a1,a2,a3,a4,a6]
Generators	[23:46:1]	Generators of the group modulo torsion
j	4533086375/60669952	j-invariant
L	2.1883791223375	L(r)(E,1)/r!
Ω	0.48338203836546	Real period
R	2.2636123693564	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	322b1 10304y1 23184bh1 64400bs1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2576n1

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	0	+	-4	0	6	6	-	10	-4	-2	-10	4	-12	-6	2	0	0	8	-6	8	14	-14	-2

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Quadratic twists for elliptic curve 2576n1

-4	8	-3	5	-7	-23
322b1	10304y1	23184bh1	64400bs1	18032ba1	59248bc1

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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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