Cremona's table of elliptic curves

1058 = 2 · 23²

Field	Data	Notes
Atkin-Lehner	2+ 23-	Signs for the Atkin-Lehner involutions
Class	1058c	Isogeny class
Conductor	1058	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	80	Modular degree for the optimal curve
Δ	-2116 = -1 · 22 · 232	Discriminant
Eigenvalues	2+ -2 -3 -2 -6 -1 -6 -2	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,0,2]	[a1,a2,a3,a4,a6]
Generators	[-1:1:1] [0:1:1]	Generators of the group modulo torsion
j	23/4	j-invariant
L	1.4760202094598	L(r)(E,1)/r!
Ω	3.5783883326878	Real period
R	0.2062409208044	Regulator
r	2	Rank of the group of rational points
S	1.0000000000009	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	8464p1 33856l1 9522n1 26450s1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1058c1

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 1058c1

-4	8	-3	5	-7	-11	-23
8464p1	33856l1	9522n1	26450s1	51842g1	128018bf1	1058b1

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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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