Cremona's table of elliptic curves

10086 = 2 · 3 · 41²

Field	Data	Notes
Atkin-Lehner	2+ 3- 41-	Signs for the Atkin-Lehner involutions
Class	10086l	Isogeny class
Conductor	10086	Conductor
∏ cp	18	Product of Tamagawa factors cp
deg	330624	Modular degree for the optimal curve
Δ	1.4129101615023E+19	Discriminant
Eigenvalues	2+ 3- -2  2  1 -5  4  6	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-1885277,979639544]	[a1,a2,a3,a4,a6]
Generators	[11907:1285054:1]	Generators of the group modulo torsion
j	92806423177/1769472	j-invariant
L	3.74342716227	L(r)(E,1)/r!
Ω	0.22281161571671	Real period
R	0.93338121090637	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	80688t1 30258z1 10086b1	Quadratic twists by: -4 -3 41

Hecke Eigenvalues for elliptic curve 10086l1

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
+	-	-2	2	1	-5	4	6	1	-6	4	-7	-	0	-8	-10	5	-11	-2	-7	13	-2	-15	-8	18

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Quadratic twists for elliptic curve 10086l1

-4	-3	41
80688t1	30258z1	10086b1

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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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