Cremona's table of elliptic curves

8092 = 2² · 7 · 17²

Field	Data	Notes
Atkin-Lehner	2- 7+ 17+	Signs for the Atkin-Lehner involutions
Class	8092a	Isogeny class
Conductor	8092	Conductor
∏ cp	3	Product of Tamagawa factors cp
deg	146880	Modular degree for the optimal curve
Δ	8673999228120663808 = 28 · 75 · 1710	Discriminant
Eigenvalues	2-  1  2 7+  4 -4 17+ -3	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-1030092,376286852]	[a1,a2,a3,a4,a6]
j	234219472/16807	j-invariant
L	2.7273176037015	L(r)(E,1)/r!
Ω	0.22727646697513	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	4	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	32368bb1 129472h1 72828q1 56644j1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 8092a1

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
-	1	2	+	4	-4	+	-3	6	-3	5	10	6	-6	-5	5	3	6	10	14	10	-12	-5	-2	12

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Quadratic twists for elliptic curve 8092a1

-4	8	-3	-7	17
32368bb1	129472h1	72828q1	56644j1	8092h1

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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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