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	8092d	Isogeny class
Conductor	8092	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	60480	Modular degree for the optimal curve
Δ	60929005312 = 28 · 77 · 172	Discriminant
Eigenvalues	2- -3 -2 7+  0  4 17+  1	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-283951,-58238906]	[a1,a2,a3,a4,a6]
j	34222845097047888/823543	j-invariant
L	0.82727270602843	L(r)(E,1)/r!
Ω	0.20681817650711	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	32368bg1 129472o1 72828o1 56644n1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 8092d1

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	-2	+	0	4	+	1	6	-3	9	-6	6	6	-1	13	7	10	6	-6	-2	-16	15	-14	-4

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Quadratic twists for elliptic curve 8092d1

-4	8	-3	-7	17
32368bg1	129472o1	72828o1	56644n1	8092j1

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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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