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	36	Product of Tamagawa factors cp
deg	576	Modular degree for the optimal curve
Δ	-4510142208 = -1 · 28 · 36 · 11 · 133	Discriminant
Eigenvalues	2+ 3-  0 -4 11+ 13-  0 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,359,1916]	[a1,a2,a3,a4,a6]
Generators	[-2:35:1]	Generators of the group modulo torsion
j	5137417856375/4510142208	j-invariant
L	1.9329491675508	L(r)(E,1)/r!
Ω	0.89640199214111	Real period
R	2.1563418918044	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	6864q1 27456n1 2574x1 21450bp1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 858b1

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 858b1

-4	8	-3	5	-7	-11	13
6864q1	27456n1	2574x1	21450bp1	42042h1	9438z1	11154bg1

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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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