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	8085g	Isogeny class
Conductor	8085	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	38455866937805625 = 36 · 54 · 78 · 114	Discriminant
Eigenvalues	-1 3+ 5+ 7- 11+  2 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-9338176,10979616248]	[a1,a2,a3,a4,a6]
j	765458482133960722801/326869475625	j-invariant
L	0.59308708663122	L(r)(E,1)/r!
Ω	0.29654354331561	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	129360gk4 24255bs4 40425cg4 1155m3	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 8085g4

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	+	+	-	+	2	-2	-4	0	6	0	6	6	-4	0	-2	-4	-6	12	0	-10	8	4	-10	-10

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Quadratic twists for elliptic curve 8085g4

-4	-3	5	-7	-11
129360gk4	24255bs4	40425cg4	1155m3	88935m4

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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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