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	8085t	Isogeny class
Conductor	8085	Conductor
∏ cp	165	Product of Tamagawa factors cp
deg	443520	Modular degree for the optimal curve
Δ	9.1041351652002E+19	Discriminant
Eigenvalues	-2 3- 5- 7+ 11+  3 -4 -2	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-4188830,-3269104744]	[a1,a2,a3,a4,a6]
Generators	[-1160:5512:1]	Generators of the group modulo torsion
j	1409995418369929216/15792626953125	j-invariant
L	2.8070367259954	L(r)(E,1)/r!
Ω	0.10560155474068	Real period
R	0.16109936861903	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	129360er1 24255ba1 40425f1 8085i1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 8085t1

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	-	-	+	+	3	-4	-2	-1	1	-8	-2	9	1	-7	7	4	10	-8	-6	-14	-4	-16	6	12

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Quadratic twists for elliptic curve 8085t1

-4	-3	5	-7	-11
129360er1	24255ba1	40425f1	8085i1	88935by1

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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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