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	8085l	Isogeny class
Conductor	8085	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	156946707225 = 32 · 52 · 78 · 112	Discriminant
Eigenvalues	1 3+ 5- 7- 11-  2  2  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-6297,188784]	[a1,a2,a3,a4,a6]
j	234770924809/1334025	j-invariant
L	2.0604128117628	L(r)(E,1)/r!
Ω	1.0302064058814	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	129360hi2 24255be2 40425cp2 1155h2	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 8085l2

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	-4	-6	4	-2	6	-4	-8	2	12	2	-4	16	-2	-4	0	-6	-14

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Quadratic twists for elliptic curve 8085l2

-4	-3	5	-7	-11
129360hi2	24255be2	40425cp2	1155h2	88935bi2

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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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