Cremona's table of elliptic curves

2809 = 53²

Field	Data	Notes
Atkin-Lehner	53+	Signs for the Atkin-Lehner involutions
Class	2809a	Isogeny class
Conductor	2809	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	5616	Modular degree for the optimal curve
Δ	-1174711139837 = -1 · 537	Discriminant
Eigenvalues	1  3  0 -4  0 -3 -3  5	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,878,50957]	[a1,a2,a3,a4,a6]
Generators	[11892:244055:27]	Generators of the group modulo torsion
j	3375/53	j-invariant
L	5.6273479240664	L(r)(E,1)/r!
Ω	0.64389701806303	Real period
R	4.3697577145136	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	44944h1 25281e1 70225d1 53a1	Quadratic twists by: -4 -3 5 53

Hecke Eigenvalues for elliptic curve 2809a1

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
1	3	0	-4	0	-3	-3	5	-7	-7	-4	5	-6	-2	-2	+	-2	8	12	-1	4	1	1	-14	1

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Quadratic twists for elliptic curve 2809a1

-4	-3	5	53
44944h1	25281e1	70225d1	53a1

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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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