Cremona's table of elliptic curves

4160 = 2⁶ · 5 · 13

Field	Data	Notes
Atkin-Lehner	2+ 5+ 13+	Signs for the Atkin-Lehner involutions
Class	4160b	Isogeny class
Conductor	4160	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	-2024510429593600 = -1 · 224 · 52 · 136	Discriminant
Eigenvalues	2+  2 5+ -4  6 13+ -6 -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,7199,-2154399]	[a1,a2,a3,a4,a6]
Generators	[18867:500480:27]	Generators of the group modulo torsion
j	157376536199/7722894400	j-invariant
L	4.4005376534564	L(r)(E,1)/r!
Ω	0.22298783225124	Real period
R	4.9336073733591	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	4160n4 130a4 37440cl4 20800be4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4160b4

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

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Quadratic twists for elliptic curve 4160b4

-4	8	-3	5	13
4160n4	130a4	37440cl4	20800be4	54080bn4

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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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