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	6	Product of Tamagawa factors cp
deg	288000	Modular degree for the optimal curve
Δ	-1998539751464746875 = -1 · 35 · 55 · 711 · 113	Discriminant
Eigenvalues	-2 3+ 5+ 7- 11-  6  7  5	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-438076,-130549434]	[a1,a2,a3,a4,a6]
Generators	[810:6737:1]	Generators of the group modulo torsion
j	-79028701534867456/16987307596875	j-invariant
L	1.9540898007023	L(r)(E,1)/r!
Ω	0.091731218898427	Real period
R	3.5503903399671	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	129360gd1 24255bo1 40425cs1 1155n1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 8085j1

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 8085j1

-4	-3	5	-7	-11
129360gd1	24255bo1	40425cs1	1155n1	88935s1

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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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