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	986d	Isogeny class
Conductor	986	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	96	Modular degree for the optimal curve
Δ	-134096 = -1 · 24 · 172 · 29	Discriminant
Eigenvalues	2-  1 -3 -2 -1 -3 17+  4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,8,16]	[a1,a2,a3,a4,a6]
Generators	[6:14:1]	Generators of the group modulo torsion
j	56181887/134096	j-invariant
L	3.2671750193093	L(r)(E,1)/r!
Ω	2.2888169877624	Real period
R	0.17843142531589	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	7888c1 31552a1 8874f1 24650j1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 986d1

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	-3	-2	-1	-3	+	4	-6	-	-7	-6	6	-3	7	11	-2	-8	-2	-2	8	3	0	-4	18

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Quadratic twists for elliptic curve 986d1

-4	8	-3	5	-7	-11	17	29
7888c1	31552a1	8874f1	24650j1	48314u1	119306h1	16762e1	28594d1

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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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