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	8085w	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 -6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-2745,-52200]	[a1,a2,a3,a4,a6]
j	19443408769/1334025	j-invariant
L	1.3248420925197	L(r)(E,1)/r!
Ω	0.66242104625983	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	129360fk2 24255bh2 40425j2 1155a2	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 8085w2

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	-6	-4	0	-6	0	6	10	4	-8	-6	8	-2	-8	-8	14	4	16	10	2

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Quadratic twists for elliptic curve 8085w2

-4	-3	5	-7	-11
129360fk2	24255bh2	40425j2	1155a2	88935cg2

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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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