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	686	Product of Tamagawa factors cp
deg	35280	Modular degree for the optimal curve
Δ	-2.6211168887701E+19	Discriminant
Eigenvalues	2- 3- -1  1 11- 13+  4  6	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-5774401,5346023177]	[a1,a2,a3,a4,a6]
j	-21293376668673906679951249/26211168887701209984	j-invariant
L	2.9529326224263	L(r)(E,1)/r!
Ω	0.21092375874473	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	7	Number of elements in the torsion subgroup
Twists	6864j1 27456g1 2574d1 21450i1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 858k1

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 858k1

-4	8	-3	5	-7	-11	13
6864j1	27456g1	2574d1	21450i1	42042cn1	9438m1	11154m1

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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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