Cremona's table of elliptic curves

16590 = 2 · 3 · 5 · 7 · 79

Field	Data	Notes
Atkin-Lehner	2+ 3- 5- 7+ 79+	Signs for the Atkin-Lehner involutions
Class	16590k	Isogeny class
Conductor	16590	Conductor
∏ cp	24	Product of Tamagawa factors cp
deg	18432	Modular degree for the optimal curve
Δ	-169100144640 = -1 · 212 · 33 · 5 · 72 · 792	Discriminant
Eigenvalues	2+ 3- 5- 7+  2  2 -2  0	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-1548,30538]	[a1,a2,a3,a4,a6]
Generators	[17:87:1]	Generators of the group modulo torsion
j	-409857819530041/169100144640	j-invariant
L	4.7732434659461	L(r)(E,1)/r!
Ω	0.95484374817595	Real period
R	0.83316310043126	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	49770bj1 82950bv1 116130c1	Quadratic twists by: -3 5 -7

Hecke Eigenvalues for elliptic curve 16590k1

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

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Quadratic twists for elliptic curve 16590k1

-3	5	-7
49770bj1	82950bv1	116130c1

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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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