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	2576p	Isogeny class
Conductor	2576	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	960	Modular degree for the optimal curve
Δ	675282944 = 222 · 7 · 23	Discriminant
Eigenvalues	2-  2 -2 7-  2 -4 -6  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-224,-256]	[a1,a2,a3,a4,a6]
Generators	[34:174:1]	Generators of the group modulo torsion
j	304821217/164864	j-invariant
L	3.96477904547	L(r)(E,1)/r!
Ω	1.3145780097007	Real period
R	3.016008952084	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	322d1 10304bg1 23184by1 64400bl1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2576p1

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

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Quadratic twists for elliptic curve 2576p1

-4	8	-3	5	-7	-23
322d1	10304bg1	23184by1	64400bl1	18032u1	59248u1

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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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