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	558c	Isogeny class
Conductor	558	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	45198 = 2 · 36 · 31	Discriminant
Eigenvalues	2+ 3-  2  0  0  2  6  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-2976,-61750]	[a1,a2,a3,a4,a6]
j	3999236143617/62	j-invariant
L	1.292749798251	L(r)(E,1)/r!
Ω	0.6463748991255	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	4	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	4464x4 17856q3 62a4 13950cc3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 558c3

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	0	0	2	6	4	-8	-2	+	10	6	8	8	6	12	-6	-12	-8	10	-8	-8	6	2

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Quadratic twists for elliptic curve 558c3

-4	8	-3	5	-7	-11	13	-31
4464x4	17856q3	62a4	13950cc3	27342q4	67518bo4	94302cg4	17298i4

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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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