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	986f	Isogeny class
Conductor	986	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	64	Modular degree for the optimal curve
Δ	-126208 = -1 · 28 · 17 · 29	Discriminant
Eigenvalues	2-  0 -2 -1  0 -1 17- -7	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-1,17]	[a1,a2,a3,a4,a6]
Generators	[-1:4:1]	Generators of the group modulo torsion
j	-35937/126208	j-invariant
L	3.0414018081344	L(r)(E,1)/r!
Ω	2.64878063725	Real period
R	0.14352839214783	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	7888e1 31552j1 8874c1 24650b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 986f1

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
-	0	-2	-1	0	-1	-	-7	-4	+	4	-3	-5	-1	-3	-3	-2	15	4	9	3	-14	6	8	2

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Quadratic twists for elliptic curve 986f1

-4	8	-3	5	-7	-11	17	29
7888e1	31552j1	8874c1	24650b1	48314p1	119306d1	16762h1	28594a1

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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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