Cremona's table of elliptic curves

13160 = 2³ · 5 · 7 · 47

Field	Data	Notes
Atkin-Lehner	2+ 5+ 7+ 47-	Signs for the Atkin-Lehner involutions
Class	13160b	Isogeny class
Conductor	13160	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	28864	Modular degree for the optimal curve
Δ	-28787500000000 = -1 · 28 · 511 · 72 · 47	Discriminant
Eigenvalues	2+  2 5+ 7+  4 -3  6  2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,7359,-89659]	[a1,a2,a3,a4,a6]
j	172139738479616/112451171875	j-invariant
L	3.030837617301	L(r)(E,1)/r!
Ω	0.37885470216263	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	26320c1 105280p1 118440cg1 65800h1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 13160b1

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	+	+	4	-3	6	2	-1	2	0	-4	6	-9	-	12	-5	1	-4	9	-1	1	12	-11	12

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Quadratic twists for elliptic curve 13160b1

-4	8	-3	5	-7
26320c1	105280p1	118440cg1	65800h1	92120j1

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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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