Cremona's table of elliptic curves

1058 = 2 · 23²

Field	Data	Notes
Atkin-Lehner	2+ 23-	Signs for the Atkin-Lehner involutions
Class	1058a	Isogeny class
Conductor	1058	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	2640	Modular degree for the optimal curve
Δ	-3486541257728 = -1 · 210 · 237	Discriminant
Eigenvalues	2+  0 -4  4 -2 -2  2  2	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-5389,178149]	[a1,a2,a3,a4,a6]
j	-116930169/23552	j-invariant
L	0.75833012807677	L(r)(E,1)/r!
Ω	0.75833012807677	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	8464m1 33856d1 9522p1 26450l1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1058a1

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
+	0	-4	4	-2	-2	2	2	-	2	0	4	6	-10	0	4	12	8	10	0	6	12	-14	6	-6

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Quadratic twists for elliptic curve 1058a1

-4	8	-3	5	-7	-11	-23
8464m1	33856d1	9522p1	26450l1	51842d1	128018t1	46a1

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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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