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	858f	Isogeny class
Conductor	858	Conductor
∏ cp	110	Product of Tamagawa factors cp
deg	2640	Modular degree for the optimal curve
Δ	-6097712265216 = -1 · 211 · 36 · 11 · 135	Discriminant
Eigenvalues	2- 3+ -3  1 11+ 13- -8 -6	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-572,118685]	[a1,a2,a3,a4,a6]
Generators	[-9:355:1]	Generators of the group modulo torsion
j	-20699471212993/6097712265216	j-invariant
L	2.596908281953	L(r)(E,1)/r!
Ω	0.61449505956969	Real period
R	0.038418953482223	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	6864ba1 27456bf1 2574n1 21450t1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 858f1

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
-	+	-3	1	+	-	-8	-6	-1	1	0	6	-11	-11	-12	2	7	11	9	-2	-11	6	14	0	6

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Quadratic twists for elliptic curve 858f1

-4	8	-3	5	-7	-11	13
6864ba1	27456bf1	2574n1	21450t1	42042db1	9438f1	11154j1

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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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