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	2576b	Isogeny class
Conductor	2576	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	3840	Modular degree for the optimal curve
Δ	-4816166591488 = -1 · 210 · 75 · 234	Discriminant
Eigenvalues	2+  2  0 7+  0  0 -6 -6	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,4192,-16816]	[a1,a2,a3,a4,a6]
Generators	[166:2286:1]	Generators of the group modulo torsion
j	7953970437500/4703287687	j-invariant
L	4.163058483994	L(r)(E,1)/r!
Ω	0.45125674184855	Real period
R	4.6127382683971	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	1288f1 10304u1 23184h1 64400v1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2576b1

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	+	0	0	-6	-6	+	-6	-8	2	-2	8	8	-2	6	0	12	8	-6	16	-6	6	-14

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Quadratic twists for elliptic curve 2576b1

-4	8	-3	5	-7	-23
1288f1	10304u1	23184h1	64400v1	18032f1	59248m1

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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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