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	8092b	Isogeny class
Conductor	8092	Conductor
∏ cp	3	Product of Tamagawa factors cp
deg	864	Modular degree for the optimal curve
Δ	517888 = 28 · 7 · 172	Discriminant
Eigenvalues	2- -1  0 7+ -6 -4 17+ -1	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-28,56]	[a1,a2,a3,a4,a6]
Generators	[-2:10:1] [2:2:1]	Generators of the group modulo torsion
j	34000/7	j-invariant
L	4.6176236844725	L(r)(E,1)/r!
Ω	2.7763756092114	Real period
R	0.55439468986748	Regulator
r	2	Rank of the group of rational points
S	0.99999999999985	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	32368x1 129472c1 72828k1 56644f1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 8092b1

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	0	+	-6	-4	+	-1	-6	-3	-5	-2	-6	8	-3	-3	-15	-8	-4	12	-8	-2	9	0	-8

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Quadratic twists for elliptic curve 8092b1

-4	8	-3	-7	17
32368x1	129472c1	72828k1	56644f1	8092g1

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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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