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	16	Product of Tamagawa factors cp
Δ	2802276 = 22 · 36 · 312	Discriminant
Eigenvalues	2+ 3-  2  0  0  2  6  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-186,-928]	[a1,a2,a3,a4,a6]
j	979146657/3844	j-invariant
L	1.292749798251	L(r)(E,1)/r!
Ω	1.292749798251	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	4464x2 17856q2 62a2 13950cc2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 558c2

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 558c2

-4	8	-3	5	-7	-11	13	-31
4464x2	17856q2	62a2	13950cc2	27342q2	67518bo2	94302cg2	17298i2

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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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