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	8085f	Isogeny class
Conductor	8085	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	1675137563810813025 = 38 · 52 · 78 · 116	Discriminant
Eigenvalues	1 3+ 5+ 7- 11+ -6 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-1762163,-898940832]	[a1,a2,a3,a4,a6]
j	5143681768032498601/14238434358225	j-invariant
L	0.26211402334541	L(r)(E,1)/r!
Ω	0.13105701167271	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	129360ha2 24255bx2 40425ck2 1155l2	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 8085f2

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
1	+	+	-	+	-6	-2	-4	-4	-2	-4	-2	-6	4	-8	-2	8	-10	-8	0	14	-16	4	6	-18

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Quadratic twists for elliptic curve 8085f2

-4	-3	5	-7	-11
129360ha2	24255bx2	40425ck2	1155l2	88935o2

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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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