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	1	Product of Tamagawa factors cp
Δ	7722 = 2 · 33 · 11 · 13	Discriminant
Eigenvalues	2- 3+ -2  0 11- 13-  6  0	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-41184,3199767]	[a1,a2,a3,a4,a6]
j	7725203825376001537/7722	j-invariant
L	1.8422546597096	L(r)(E,1)/r!
Ω	1.8422546597096	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	4	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	6864w3 27456y4 2574j3 21450bb4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 858h4

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 858h4

-4	8	-3	5	-7	-11	13
6864w3	27456y4	2574j3	21450bb4	42042dm4	9438e3	11154d4

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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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