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	17661d	Isogeny class
Conductor	17661	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	41760	Modular degree for the optimal curve
Δ	94546572049629 = 33 · 7 · 298	Discriminant
Eigenvalues	-1 3+  1 7- -2 -2  5  2	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-14735,498944]	[a1,a2,a3,a4,a6]
Generators	[-76:1127:1]	Generators of the group modulo torsion
j	707281/189	j-invariant
L	2.8846092288489	L(r)(E,1)/r!
Ω	0.56147936211293	Real period
R	5.1375160397592	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	52983j1 123627x1 17661e1	Quadratic twists by: -3 -7 29

Hecke Eigenvalues for elliptic curve 17661d1

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	+	1	-	-2	-2	5	2	6	-	4	5	-9	3	-8	-6	3	2	3	-10	-10	-12	1	15	-12

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Quadratic twists for elliptic curve 17661d1

-3	-7	29
52983j1	123627x1	17661e1

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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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