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	16	Product of Tamagawa factors cp
Δ	62035801809135 = 3 · 5 · 710 · 114	Discriminant
Eigenvalues	1 3+ 5- 7- 11-  2  2  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-9972,-61851]	[a1,a2,a3,a4,a6]
j	932288503609/527295615	j-invariant
L	2.0604128117628	L(r)(E,1)/r!
Ω	0.51510320294071	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	129360hi3 24255be3 40425cp3 1155h4	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 8085l3

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 8085l3

-4	-3	5	-7	-11
129360hi3	24255be3	40425cp3	1155h4	88935bi3

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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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