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	858g	Isogeny class
Conductor	858	Conductor
∏ cp	18	Product of Tamagawa factors cp
deg	144	Modular degree for the optimal curve
Δ	-658944 = -1 · 29 · 32 · 11 · 13	Discriminant
Eigenvalues	2- 3+ -1 -3 11- 13+ -4 -2	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-46,107]	[a1,a2,a3,a4,a6]
Generators	[5:-9:1]	Generators of the group modulo torsion
j	-10779215329/658944	j-invariant
L	2.6549896365849	L(r)(E,1)/r!
Ω	2.8332583986387	Real period
R	0.052059997184014	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	6864t1 27456bb1 2574e1 21450be1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 858g1

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	-3	-	+	-4	-2	-1	-9	-4	-6	1	11	0	-10	-3	5	3	10	9	10	-6	-8	2

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Quadratic twists for elliptic curve 858g1

-4	8	-3	5	-7	-11	13
6864t1	27456bb1	2574e1	21450be1	42042dp1	9438h1	11154b1

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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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