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	17661g	Isogeny class
Conductor	17661	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	31515524016543 = 32 · 7 · 298	Discriminant
Eigenvalues	-1 3-  0 7-  0 -6  2  0	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-29873,1966386]	[a1,a2,a3,a4,a6]
Generators	[447:8607:1]	Generators of the group modulo torsion
j	4956477625/52983	j-invariant
L	3.603557325669	L(r)(E,1)/r!
Ω	0.66151403631854	Real period
R	2.7237194736816	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	52983b2 123627f2 609a2	Quadratic twists by: -3 -7 29

Hecke Eigenvalues for elliptic curve 17661g2

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	-	0	-	0	-6	2	0	-6	+	4	-6	10	10	-8	10	-12	8	12	14	-16	14	4	6	8

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Quadratic twists for elliptic curve 17661g2

-3	-7	29
52983b2	123627f2	609a2

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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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