Cremona's table of elliptic curves

986 = 2 · 17 · 29

Field	Data	Notes
Atkin-Lehner	2+ 17- 29-	Signs for the Atkin-Lehner involutions
Class	986b	Isogeny class
Conductor	986	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	864	Modular degree for the optimal curve
Δ	-34328576 = -1 · 212 · 172 · 29	Discriminant
Eigenvalues	2+ -1  1 -2  1  5 17- -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-10407,-413003]	[a1,a2,a3,a4,a6]
Generators	[126:481:1]	Generators of the group modulo torsion
j	-124671038996895481/34328576	j-invariant
L	1.631689770791	L(r)(E,1)/r!
Ω	0.23633755028367	Real period
R	1.7260162094773	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	7888h1 31552e1 8874h1 24650bd1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 986b1

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	1	-2	1	5	-	-4	-6	-	-1	2	2	-9	-3	3	6	-12	10	-14	-8	-11	-12	-16	-2

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Quadratic twists for elliptic curve 986b1

-4	8	-3	5	-7	-11	17	29
7888h1	31552e1	8874h1	24650bd1	48314f1	119306p1	16762a1	28594h1

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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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