Cremona's table of elliptic curves

2597 = 7² · 53

Field	Data	Notes
Atkin-Lehner	7- 53+	Signs for the Atkin-Lehner involutions
Class	2597c	Isogeny class
Conductor	2597	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	1848	Modular degree for the optimal curve
Δ	14971188197 = 710 · 53	Discriminant
Eigenvalues	1 -2  0 7- -3  5 -5 -2	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-1251,-16075]	[a1,a2,a3,a4,a6]
j	765625/53	j-invariant
L	0.80633469041891	L(r)(E,1)/r!
Ω	0.80633469041891	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	41552bi1 23373i1 64925k1 2597a1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 2597c1

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	-2	0	-	-3	5	-5	-2	4	-9	-4	-9	10	3	-3	+	11	14	4	-2	14	4	-4	15	-10

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Quadratic twists for elliptic curve 2597c1

-4	-3	5	-7
41552bi1	23373i1	64925k1	2597a1

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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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