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	558a	Isogeny class
Conductor	558	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	16	Modular degree for the optimal curve
Δ	-1674 = -1 · 2 · 33 · 31	Discriminant
Eigenvalues	2+ 3+ -1  0 -3 -1 -3  1	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,0,2]	[a1,a2,a3,a4,a6]
Generators	[1:1:1]	Generators of the group modulo torsion
j	-27/62	j-invariant
L	1.5014219877569	L(r)(E,1)/r!
Ω	3.8035017776737	Real period
R	0.1973736408604	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	4464p1 17856a1 558e1 13950bs1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 558a1

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	0	-3	-1	-3	1	-2	-2	+	-2	0	-4	-7	0	6	-9	3	1	-8	1	-5	6	-7

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Quadratic twists for elliptic curve 558a1

-4	8	-3	5	-7	-11	13	-31
4464p1	17856a1	558e1	13950bs1	27342b1	67518bb1	94302bm1	17298c1

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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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