Cremona's table of elliptic curves

2583 = 3² · 7 · 41

Field	Data	Notes
Atkin-Lehner	3- 7- 41-	Signs for the Atkin-Lehner involutions
Class	2583f	Isogeny class
Conductor	2583	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	640	Modular degree for the optimal curve
Δ	-50841189 = -1 · 311 · 7 · 41	Discriminant
Eigenvalues	1 3-  3 7-  2  5  2 -2	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-63,-378]	[a1,a2,a3,a4,a6]
j	-38272753/69741	j-invariant
L	3.1931603935505	L(r)(E,1)/r!
Ω	0.79829009838763	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	41328bq1 861d1 64575u1 18081j1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 2583f1

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	-	2	5	2	-2	3	-1	-8	1	-	-10	9	11	4	2	-5	6	4	11	-14	-8	1

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Quadratic twists for elliptic curve 2583f1

-4	-3	5	-7	41
41328bq1	861d1	64575u1	18081j1	105903e1

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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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