Cremona's table of elliptic curves

17661 = 3 · 7 · 29²

Field	Data	Notes
Atkin-Lehner	3- 7- 29+	Signs for the Atkin-Lehner involutions
Class	17661f	Isogeny class
Conductor	17661	Conductor
∏ cp	48	Product of Tamagawa factors cp
deg	322560	Modular degree for the optimal curve
Δ	-2684936813291986743 = -1 · 33 · 78 · 297	Discriminant
Eigenvalues	1 3- -2 7- -4 -2 -2  4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-659362,220588751]	[a1,a2,a3,a4,a6]
Generators	[427:3902:1]	Generators of the group modulo torsion
j	-53297461115137/4513839183	j-invariant
L	5.743638979194	L(r)(E,1)/r!
Ω	0.25040673774069	Real period
R	1.911436512923	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	52983h1 123627e1 609b1	Quadratic twists by: -3 -7 29

Hecke Eigenvalues for elliptic curve 17661f1

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	-	-2	-	-4	-2	-2	4	0	+	8	10	6	-12	8	6	12	10	-12	-16	-2	0	4	6	6

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Quadratic twists for elliptic curve 17661f1

-3	-7	29
52983h1	123627e1	609b1

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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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