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	17661i	Isogeny class
Conductor	17661	Conductor
∏ cp	143	Product of Tamagawa factors cp
deg	686400	Modular degree for the optimal curve
Δ	1.4434585519844E+19	Discriminant
Eigenvalues	-1 3- -3 7-  6 -6 -1  6	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-1089997,397955876]	[a1,a2,a3,a4,a6]
Generators	[-229:25325:1]	Generators of the group modulo torsion
j	170295687079857398473/17163597526568829	j-invariant
L	3.3111567903163	L(r)(E,1)/r!
Ω	0.21591063613004	Real period
R	0.10724317710628	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	52983e1 123627j1 17661c1	Quadratic twists by: -3 -7 29

Hecke Eigenvalues for elliptic curve 17661i1

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	-	6	-6	-1	6	6	+	4	3	-11	-11	-8	10	-9	2	3	-10	2	-4	-11	-3	-16

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Quadratic twists for elliptic curve 17661i1

-3	-7	29
52983e1	123627j1	17661c1

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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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