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	8085i	Isogeny class
Conductor	8085	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	63360	Modular degree for the optimal curve
Δ	773838720703125 = 35 · 511 · 72 · 113	Discriminant
Eigenvalues	-2 3+ 5+ 7- 11+ -3  4  2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-85486,9555342]	[a1,a2,a3,a4,a6]
j	1409995418369929216/15792626953125	j-invariant
L	0.50653264397761	L(r)(E,1)/r!
Ω	0.50653264397761	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	129360gp1 24255bz1 40425cl1 8085t1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 8085i1

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 8085i1

-4	-3	5	-7	-11
129360gp1	24255bz1	40425cl1	8085t1	88935q1

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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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