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	4160h	Isogeny class
Conductor	4160	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	-11698585600 = -1 · 214 · 52 · 134	Discriminant
Eigenvalues	2+ -2 5-  2 -4 13-  2  0	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-1105,14703]	[a1,a2,a3,a4,a6]
Generators	[13:52:1]	Generators of the group modulo torsion
j	-9115564624/714025	j-invariant
L	2.8263406752162	L(r)(E,1)/r!
Ω	1.2476327561059	Real period
R	0.56634066823434	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	4160p2 260a2 37440br2 20800m2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4160h2

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	-4	-	2	0	-6	10	0	-10	-2	-2	-6	-2	8	-2	6	-8	10	-16	-6	10	2

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Quadratic twists for elliptic curve 4160h2

-4	8	-3	5	13
4160p2	260a2	37440br2	20800m2	54080r2

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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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