Cremona's table of elliptic curves

2597 = 7² · 53

Field	Data	Notes
Atkin-Lehner	7+ 53+	Signs for the Atkin-Lehner involutions
Class	2597a	Isogeny class
Conductor	2597	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	264	Modular degree for the optimal curve
Δ	127253 = 74 · 53	Discriminant
Eigenvalues	1  2  0 7+ -3 -5  5  2	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-25,36]	[a1,a2,a3,a4,a6]
Generators	[0:6:1]	Generators of the group modulo torsion
j	765625/53	j-invariant
L	4.9930236745591	L(r)(E,1)/r!
Ω	3.2338057808126	Real period
R	1.5440085190597	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	41552t1 23373b1 64925c1 2597c1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 2597a1

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 2597a1

-4	-3	5	-7
41552t1	23373b1	64925c1	2597c1

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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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