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	558f	Isogeny class
Conductor	558	Conductor
∏ cp	30	Product of Tamagawa factors cp
Δ	-18764040096 = -1 · 25 · 39 · 313	Discriminant
Eigenvalues	2- 3+ -3 -4 -3  5 -3 -7	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-434,-7343]	[a1,a2,a3,a4,a6]
Generators	[91:-883:1]	Generators of the group modulo torsion
j	-458314011/953312	j-invariant
L	2.3825303331677	L(r)(E,1)/r!
Ω	0.49077570641057	Real period
R	0.16182071918983	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	4464n2 17856i2 558b1 13950i2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 558f2

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	-4	-3	5	-3	-7	-6	-6	-	2	12	8	3	-12	-6	5	11	3	-4	-13	3	6	-7

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Quadratic twists for elliptic curve 558f2

-4	8	-3	5	-7	-11	13	-31
4464n2	17856i2	558b1	13950i2	27342w2	67518f2	94302d2	17298n2

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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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