Cremona's table of elliptic curves

858 = 2 · 3 · 11 · 13

Field	Data	Notes
Atkin-Lehner	2- 3+ 11- 13-	Signs for the Atkin-Lehner involutions
Class	858h	Isogeny class
Conductor	858	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	333926700822 = 2 · 312 · 11 · 134	Discriminant
Eigenvalues	2- 3+ -2  0 11- 13-  6  0	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-2684,44615]	[a1,a2,a3,a4,a6]
j	2138362647385537/333926700822	j-invariant
L	1.8422546597096	L(r)(E,1)/r!
Ω	0.92112732985481	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	6864w4 27456y3 2574j4 21450bb3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 858h3

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

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Quadratic twists for elliptic curve 858h3

-4	8	-3	5	-7	-11	13
6864w4	27456y3	2574j4	21450bb3	42042dm3	9438e4	11154d3

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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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