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	8	Product of Tamagawa factors cp
Δ	3678951124992 = 212 · 3 · 116 · 132	Discriminant
Eigenvalues	2+ 3-  0 -4 11+ 13-  0 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-65176,-6409114]	[a1,a2,a3,a4,a6]
Generators	[585:12187:1]	Generators of the group modulo torsion
j	30618029936661765625/3678951124992	j-invariant
L	1.9329491675508	L(r)(E,1)/r!
Ω	0.29880066404704	Real period
R	3.2345128377066	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	6864q4 27456n4 2574x4 21450bp4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 858b4

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 858b4

-4	8	-3	5	-7	-11	13
6864q4	27456n4	2574x4	21450bp4	42042h4	9438z4	11154bg4

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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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