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	16	Product of Tamagawa factors cp
Δ	3397517312 = 217 · 72 · 232	Discriminant
Eigenvalues	2-  2 -2 7-  2 -4 -6  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-2784,-55552]	[a1,a2,a3,a4,a6]
Generators	[176:2208:1]	Generators of the group modulo torsion
j	582810602977/829472	j-invariant
L	3.96477904547	L(r)(E,1)/r!
Ω	0.65728900485035	Real period
R	1.508004476042	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	322d2 10304bg2 23184by2 64400bl2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2576p2

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 2576p2

-4	8	-3	5	-7	-23
322d2	10304bg2	23184by2	64400bl2	18032u2	59248u2

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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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