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	858l	Isogeny class
Conductor	858	Conductor
∏ cp	28	Product of Tamagawa factors cp
Δ	61165323648 = 27 · 32 · 11 · 136	Discriminant
Eigenvalues	2- 3-  2  4 11- 13+ -8 -6	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-7372,-243952]	[a1,a2,a3,a4,a6]
j	44308125149913793/61165323648	j-invariant
L	3.6069237303691	L(r)(E,1)/r!
Ω	0.51527481862416	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	6864k2 27456k2 2574f2 21450l2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 858l2

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	4	-	+	-8	-6	-6	-2	-2	4	2	4	4	-8	12	-2	12	-16	0	-8	4	10	10

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Quadratic twists for elliptic curve 858l2

-4	8	-3	5	-7	-11	13
6864k2	27456k2	2574f2	21450l2	42042cp2	9438o2	11154o2

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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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