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	8085k	Isogeny class
Conductor	8085	Conductor
∏ cp	6	Product of Tamagawa factors cp
Δ	-411050899875 = -1 · 3 · 53 · 77 · 113	Discriminant
Eigenvalues	0 3+ 5- 7- 11+  4 -3  1	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-41225,3235658]	[a1,a2,a3,a4,a6]
Generators	[124:122:1]	Generators of the group modulo torsion
j	-65860951343104/3493875	j-invariant
L	3.1215931537153	L(r)(E,1)/r!
Ω	0.89329748270689	Real period
R	0.58241015528522	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	129360id2 24255bg2 40425cc2 1155j2	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 8085k2

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
0	+	-	-	+	4	-3	1	-3	-9	10	-4	-6	-1	6	-9	-15	13	2	-6	16	8	3	9	-17

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Quadratic twists for elliptic curve 8085k2

-4	-3	5	-7	-11
129360id2	24255bg2	40425cc2	1155j2	88935bh2

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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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