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	128	Product of Tamagawa factors cp
Δ	71508843479390625 = 38 · 56 · 78 · 112	Discriminant
Eigenvalues	1 3- 5+ 7- 11+  2  6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-796129,273046127]	[a1,a2,a3,a4,a6]
Generators	[1:16499:1]	Generators of the group modulo torsion
j	474334834335054841/607815140625	j-invariant
L	5.6763662188831	L(r)(E,1)/r!
Ω	0.34512649404398	Real period
R	2.0559006323924	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	129360eh2 24255bu2 40425m2 1155f2	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 8085n2

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 8085n2

-4	-3	5	-7	-11
129360eh2	24255bu2	40425m2	1155f2	88935br2

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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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