Cremona's table of elliptic curves

2573 = 31 · 83

Field	Data	Notes
Atkin-Lehner	31- 83+	Signs for the Atkin-Lehner involutions
Class	2573a	Isogeny class
Conductor	2573	Conductor
∏ cp	3	Product of Tamagawa factors cp
deg	936	Modular degree for the optimal curve
Δ	2472653 = 313 · 83	Discriminant
Eigenvalues	2  2  4 -3  0  3  2  2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-36,49]	[a1,a2,a3,a4,a6]
j	5304438784/2472653	j-invariant
L	6.9065781509127	L(r)(E,1)/r!
Ω	2.3021927169709	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	41168e1 23157f1 64325d1 126077b1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 2573a1

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	2	4	-3	0	3	2	2	8	2	-	-8	-2	-11	6	-6	11	-4	-2	8	6	5	+	-15	-2

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Quadratic twists for elliptic curve 2573a1

-4	-3	5	-7	-31
41168e1	23157f1	64325d1	126077b1	79763e1

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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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