Cremona's table of elliptic curves

8085 = 3 · 5 · 7² · 11

Field	Data	Notes
Atkin-Lehner	3- 5+ 7- 11+	Signs for the Atkin-Lehner involutions
Class	8085n	Isogeny class
Conductor	8085	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	55296	Modular degree for the optimal curve
Δ	91722101625 = 34 · 53 · 77 · 11	Discriminant
Eigenvalues	1 3- 5+ 7- 11+  2  6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-795884,273222821]	[a1,a2,a3,a4,a6]
Generators	[579:2278:1]	Generators of the group modulo torsion
j	473897054735271721/779625	j-invariant
L	5.6763662188831	L(r)(E,1)/r!
Ω	0.69025298808797	Real period
R	4.1118012647847	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	129360eh1 24255bu1 40425m1 1155f1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 8085n1

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	6	-4	-4	-2	4	-2	2	-12	0	-2	0	14	-8	-16	-10	16	4	6	-2

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Quadratic twists for elliptic curve 8085n1

-4	-3	5	-7	-11
129360eh1	24255bu1	40425m1	1155f1	88935br1

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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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