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	858j	Isogeny class
Conductor	858	Conductor
∏ cp	18	Product of Tamagawa factors cp
deg	240	Modular degree for the optimal curve
Δ	-833976 = -1 · 23 · 36 · 11 · 13	Discriminant
Eigenvalues	2- 3- -3  5 11+ 13-  0  2	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,13,-39]	[a1,a2,a3,a4,a6]
j	241804367/833976	j-invariant
L	2.8733803996711	L(r)(E,1)/r!
Ω	1.4366901998355	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	6864s1 27456r1 2574o1 21450e1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 858j1

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	5	+	-	0	2	3	-3	8	-10	-3	5	12	-6	-9	-13	5	6	-7	-10	6	0	-10

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Quadratic twists for elliptic curve 858j1

-4	8	-3	5	-7	-11	13
6864s1	27456r1	2574o1	21450e1	42042cb1	9438l1	11154u1

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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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