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	16	Product of Tamagawa factors cp
Δ	306031424964608 = 211 · 710 · 232	Discriminant
Eigenvalues	2+  2  0 7+  0  0 -6 -6	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-16968,-118384]	[a1,a2,a3,a4,a6]
Generators	[-88:828:1]	Generators of the group modulo torsion
j	263822189935250/149429406721	j-invariant
L	4.163058483994	L(r)(E,1)/r!
Ω	0.45125674184855	Real period
R	2.3063691341986	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	1288f2 10304u2 23184h2 64400v2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2576b2

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 2576b2

-4	8	-3	5	-7	-23
1288f2	10304u2	23184h2	64400v2	18032f2	59248m2

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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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