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	986c	Isogeny class
Conductor	986	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	432	Modular degree for the optimal curve
Δ	58560512 = 212 · 17 · 292	Discriminant
Eigenvalues	2+  2 -2 -2 -2  2 17- -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-276,1616]	[a1,a2,a3,a4,a6]
Generators	[-1:44:1]	Generators of the group modulo torsion
j	2338337977417/58560512	j-invariant
L	2.1668844307302	L(r)(E,1)/r!
Ω	1.9736513369181	Real period
R	1.0979063982567	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	7888i1 31552h1 8874i1 24650bf1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 986c1

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	-2	-2	2	-	-4	6	-	-10	-10	2	-12	-12	6	0	6	4	10	-14	10	0	14	10

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Quadratic twists for elliptic curve 986c1

-4	8	-3	5	-7	-11	17	29
7888i1	31552h1	8874i1	24650bf1	48314j1	119306q1	16762b1	28594k1

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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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