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	858c	Isogeny class
Conductor	858	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	80	Modular degree for the optimal curve
Δ	-18876 = -1 · 22 · 3 · 112 · 13	Discriminant
Eigenvalues	2+ 3- -2  4 11- 13-  0  2	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-7,-10]	[a1,a2,a3,a4,a6]
j	-30664297/18876	j-invariant
L	1.4531272382246	L(r)(E,1)/r!
Ω	1.4531272382246	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	6864n1 27456b1 2574u1 21450bw1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 858c1

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
+	-	-2	4	-	-	0	2	-2	2	-2	12	6	0	0	4	12	-6	-4	4	4	-8	-12	10	2

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Quadratic twists for elliptic curve 858c1

-4	8	-3	5	-7	-11	13
6864n1	27456b1	2574u1	21450bw1	42042r1	9438bc1	11154bd1

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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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