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	13160d	Isogeny class
Conductor	13160	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	2560	Modular degree for the optimal curve
Δ	52640000 = 28 · 54 · 7 · 47	Discriminant
Eigenvalues	2-  0 5+ 7+  0  2 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-143,-558]	[a1,a2,a3,a4,a6]
Generators	[-7:10:1]	Generators of the group modulo torsion
j	1263257424/205625	j-invariant
L	3.8776436948296	L(r)(E,1)/r!
Ω	1.3958135333988	Real period
R	1.3890264000333	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	26320b1 105280k1 118440bc1 65800b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 13160d1

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

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Quadratic twists for elliptic curve 13160d1

-4	8	-3	5	-7
26320b1	105280k1	118440bc1	65800b1	92120q1

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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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