Cremona's table of elliptic curves

4576 = 2⁵ · 11 · 13

Field	Data	Notes
Atkin-Lehner	2- 11- 13+	Signs for the Atkin-Lehner involutions
Class	4576g	Isogeny class
Conductor	4576	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	4352	Modular degree for the optimal curve
Δ	-1286844416 = -1 · 212 · 11 · 134	Discriminant
Eigenvalues	2- -3  1  4 11- 13+ -4  2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,248,-848]	[a1,a2,a3,a4,a6]
Generators	[76:676:1]	Generators of the group modulo torsion
j	411830784/314171	j-invariant
L	2.8246503718896	L(r)(E,1)/r!
Ω	0.85366651676254	Real period
R	0.827211304539	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	4576c1 9152g1 41184h1 114400j1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4576g1

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
-	-3	1	4	-	+	-4	2	9	-8	-7	-1	-10	-10	4	-14	3	-4	-5	-13	6	10	-6	15	9

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Quadratic twists for elliptic curve 4576g1

-4	8	-3	5	-11	13
4576c1	9152g1	41184h1	114400j1	50336o1	59488h1

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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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