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	4160f	Isogeny class
Conductor	4160	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	1331200 = 212 · 52 · 13	Discriminant
Eigenvalues	2+  0 5- -2  2 13- -2 -2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-1732,-27744]	[a1,a2,a3,a4,a6]
Generators	[386:255:8]	Generators of the group modulo torsion
j	140283769536/325	j-invariant
L	3.5982040956442	L(r)(E,1)/r!
Ω	0.7400526926508	Real period
R	4.8620917555963	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	4160e2 2080b1 37440bt2 20800b2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4160f2

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	-	-2	2	-	-2	-2	4	-2	6	-2	2	-4	6	-6	-14	-6	10	-2	-14	4	-14	-14	-6

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Quadratic twists for elliptic curve 4160f2

-4	8	-3	5	13
4160e2	2080b1	37440bt2	20800b2	54080d2

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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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