Cremona's table of elliptic curves

558 = 2 · 3² · 31

Field	Data	Notes
Atkin-Lehner	2- 3- 31+	Signs for the Atkin-Lehner involutions
Class	558g	Isogeny class
Conductor	558	Conductor
∏ cp	28	Product of Tamagawa factors cp
deg	224	Modular degree for the optimal curve
Δ	-8678016 = -1 · 27 · 37 · 31	Discriminant
Eigenvalues	2- 3- -3 -2 -5 -7  1  7	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-149,749]	[a1,a2,a3,a4,a6]
Generators	[9:-14:1]	Generators of the group modulo torsion
j	-498677257/11904	j-invariant
L	2.4016041199967	L(r)(E,1)/r!
Ω	2.3163764159966	Real period
R	0.037028340956091	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	4464z1 17856t1 186c1 13950p1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 558g1

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
-	-	-3	-2	-5	-7	1	7	-4	8	+	-6	2	-10	1	-6	10	1	-3	-3	14	-11	-7	6	-3

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Quadratic twists for elliptic curve 558g1

-4	8	-3	5	-7	-11	13	-31
4464z1	17856t1	186c1	13950p1	27342bt1	67518p1	94302z1	17298v1

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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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