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	8085s	Isogeny class
Conductor	8085	Conductor
∏ cp	9	Product of Tamagawa factors cp
deg	8064	Modular degree for the optimal curve
Δ	8560729485 = 33 · 5 · 78 · 11	Discriminant
Eigenvalues	2 3- 5- 7+ 11+ -5 -4 -2	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-800,-7759]	[a1,a2,a3,a4,a6]
Generators	[-166:143:8]	Generators of the group modulo torsion
j	9834496/1485	j-invariant
L	9.7461683340118	L(r)(E,1)/r!
Ω	0.90668828657463	Real period
R	1.1943548942924	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	129360eu1 24255bb1 40425g1 8085h1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 8085s1

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	-	-	+	+	-5	-4	-2	3	-3	0	-6	-3	-7	-3	-5	4	-6	12	6	10	-4	-4	-14	-8

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Quadratic twists for elliptic curve 8085s1

-4	-3	5	-7	-11
129360eu1	24255bb1	40425g1	8085h1	88935bz1

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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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