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	858k	Isogeny class
Conductor	858	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	-4.8918776756543E+25	Discriminant
Eigenvalues	2- 3- -1  1 11- 13+  4  6	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,16353089,-335543012233]	[a1,a2,a3,a4,a6]
j	483641001192506212470106511/48918776756543177755473774	j-invariant
L	2.9529326224263	L(r)(E,1)/r!
Ω	0.030131965534962	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	49	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	6864j2 27456g2 2574d2 21450i2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 858k2

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
-	-	-1	1	-	+	4	6	3	-5	4	10	-7	-5	-8	-2	-3	13	-9	2	-3	10	-14	-8	-14

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Quadratic twists for elliptic curve 858k2

-4	8	-3	5	-7	-11	13
6864j2	27456g2	2574d2	21450i2	42042cn2	9438m2	11154m2

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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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