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	8085y	Isogeny class
Conductor	8085	Conductor
∏ cp	50	Product of Tamagawa factors cp
deg	19200	Modular degree for the optimal curve
Δ	-161148394786995 = -1 · 35 · 5 · 77 · 115	Discriminant
Eigenvalues	0 3- 5- 7- 11-  0 -3  3	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-6435,-644416]	[a1,a2,a3,a4,a6]
Generators	[198:2425:1]	Generators of the group modulo torsion
j	-250523582464/1369738755	j-invariant
L	4.5454726487112	L(r)(E,1)/r!
Ω	0.23954268969572	Real period
R	0.37951253319274	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	129360ev1 24255bc1 40425t1 1155d1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 8085y1

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	-	-	-	-	0	-3	3	-1	-7	-6	-8	2	-5	6	-3	5	7	6	-10	-12	-16	3	-3	1

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Quadratic twists for elliptic curve 8085y1

-4	-3	5	-7	-11
129360ev1	24255bc1	40425t1	1155d1	88935ce1

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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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