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	10086q	Isogeny class
Conductor	10086	Conductor
∏ cp	132	Product of Tamagawa factors cp
deg	22176	Modular degree for the optimal curve
Δ	1219723702272 = 212 · 311 · 412	Discriminant
Eigenvalues	2- 3- -2 -2  1  1 -4  2	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-20289,1109385]	[a1,a2,a3,a4,a6]
Generators	[78:15:1]	Generators of the group modulo torsion
j	549464024729857/725594112	j-invariant
L	6.7204547213375	L(r)(E,1)/r!
Ω	0.86187561178053	Real period
R	0.059071790722248	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	80688m1 30258f1 10086o1	Quadratic twists by: -4 -3 41

Hecke Eigenvalues for elliptic curve 10086q1

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	1	-4	2	-5	2	4	5	+	4	8	-10	3	-15	2	-3	-11	14	7	-12	-10

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Quadratic twists for elliptic curve 10086q1

-4	-3	41
80688m1	30258f1	10086o1

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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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