Cremona's table of elliptic curves

1058 = 2 · 23²

Field	Data	Notes
Atkin-Lehner	2+ 23-	Signs for the Atkin-Lehner involutions
Class	1058d	Isogeny class
Conductor	1058	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	19320	Modular degree for the optimal curve
Δ	-5302593435347072 = -1 · 27 · 2310	Discriminant
Eigenvalues	2+  3  2 -2  4  4 -1 -7	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-332311,-73733731]	[a1,a2,a3,a4,a6]
j	-97967097/128	j-invariant
L	2.485360027852	L(r)(E,1)/r!
Ω	0.099414401114081	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	25	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	8464r1 33856w1 9522l1 26450v1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1058d1

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	2	-2	4	4	-1	-7	-	-4	6	-2	6	-1	6	-8	-9	-4	7	6	-9	12	-5	-6	6

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Quadratic twists for elliptic curve 1058d1

-4	8	-3	5	-7	-11	-23
8464r1	33856w1	9522l1	26450v1	51842l1	128018bi1	1058e1

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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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