Cremona's table of elliptic curves

588 = 2² · 3 · 7²

Field	Data	Notes
Atkin-Lehner	2- 3- 7-	Signs for the Atkin-Lehner involutions
Class	588d	Isogeny class
Conductor	588	Conductor
∏ cp	5	Product of Tamagawa factors cp
deg	1260	Modular degree for the optimal curve
Δ	-17572220289792 = -1 · 28 · 35 · 710	Discriminant
Eigenvalues	2- 3-  2 7-  2  3 -8  1	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,6403,44463]	[a1,a2,a3,a4,a6]
j	401408/243	j-invariant
L	2.1239731794962	L(r)(E,1)/r!
Ω	0.42479463589925	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	2352m1 9408n1 1764h1 14700d1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 588d1

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	3	-8	1	8	4	-3	-1	-6	11	-6	-12	-4	6	13	-10	11	-3	-2	0	-10

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Quadratic twists for elliptic curve 588d1

-4	8	-3	5	-7	-11	13
2352m1	9408n1	1764h1	14700d1	588a1	71148cj1	99372bp1

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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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