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	8085j	Isogeny class
Conductor	8085	Conductor
∏ cp	30	Product of Tamagawa factors cp
Δ	-5.1602152337776E+22	Discriminant
Eigenvalues	-2 3+ 5+ 7- 11-  6  7  5	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-1312726,10945050906]	[a1,a2,a3,a4,a6]
Generators	[14775:1793522:1]	Generators of the group modulo torsion
j	-2126464142970105856/438611057788643355	j-invariant
L	1.9540898007023	L(r)(E,1)/r!
Ω	0.091731218898427	Real period
R	0.71007806799343	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	129360gd2 24255bo2 40425cs2 1155n2	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 8085j2

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
-2	+	+	-	-	6	7	5	-1	-5	8	-2	-12	-11	-8	-11	5	-7	-2	12	-4	-10	1	-15	-3

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Quadratic twists for elliptic curve 8085j2

-4	-3	5	-7	-11
129360gd2	24255bo2	40425cs2	1155n2	88935s2

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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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