Cremona's table of elliptic curves

1058 = 2 · 23²

Field	Data	Notes
Atkin-Lehner	2+ 23-	Signs for the Atkin-Lehner involutions
Class	1058b	Isogeny class
Conductor	1058	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	-5011903057984 = -1 · 26 · 238	Discriminant
Eigenvalues	2+ -2  3  2  6 -1  6  2	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-60582,-5745352]	[a1,a2,a3,a4,a6]
j	-313994137/64	j-invariant
L	1.21722031666	L(r)(E,1)/r!
Ω	0.1521525395825	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	4	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	8464o2 33856n2 9522o2 26450t2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1058b2

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	3	2	6	-1	6	2	-	-9	-4	2	-9	-4	6	3	6	-1	8	6	11	8	0	-9	-1

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Quadratic twists for elliptic curve 1058b2

-4	8	-3	5	-7	-11	-23
8464o2	33856n2	9522o2	26450t2	51842h2	128018be2	1058c2

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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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