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	2	Product of Tamagawa factors cp
deg	6912	Modular degree for the optimal curve
Δ	-59925106395 = -1 · 33 · 5 · 79 · 11	Discriminant
Eigenvalues	0 3+ 5- 7- 11+  4 -3  1	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-65,11801]	[a1,a2,a3,a4,a6]
Generators	[-23:24:1]	Generators of the group modulo torsion
j	-262144/509355	j-invariant
L	3.1215931537153	L(r)(E,1)/r!
Ω	0.89329748270689	Real period
R	1.7472304658557	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	129360id1 24255bg1 40425cc1 1155j1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 8085k1

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 8085k1

-4	-3	5	-7	-11
129360id1	24255bg1	40425cc1	1155j1	88935bh1

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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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