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	858b	Isogeny class
Conductor	858	Conductor
∏ cp	72	Product of Tamagawa factors cp
Δ	252306960048 = 24 · 33 · 112 · 136	Discriminant
Eigenvalues	2+ 3-  0 -4 11+ 13-  0 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-1801,16604]	[a1,a2,a3,a4,a6]
Generators	[7:62:1]	Generators of the group modulo torsion
j	645532578015625/252306960048	j-invariant
L	1.9329491675508	L(r)(E,1)/r!
Ω	0.89640199214111	Real period
R	1.0781709459022	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	6	Number of elements in the torsion subgroup
Twists	6864q2 27456n2 2574x2 21450bp2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 858b2

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

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Quadratic twists for elliptic curve 858b2

-4	8	-3	5	-7	-11	13
6864q2	27456n2	2574x2	21450bp2	42042h2	9438z2	11154bg2

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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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