Cremona's table of elliptic curves

6160 = 2⁴ · 5 · 7 · 11

Field	Data	Notes
Atkin-Lehner	2- 5+ 7+ 11-	Signs for the Atkin-Lehner involutions
Class	6160f	Isogeny class
Conductor	6160	Conductor
∏ cp	24	Product of Tamagawa factors cp
Δ	-8753546002432000 = -1 · 230 · 53 · 72 · 113	Discriminant
Eigenvalues	2-  2 5+ 7+ 11-  2 -6 -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,36344,-3638544]	[a1,a2,a3,a4,a6]
Generators	[1218:42966:1]	Generators of the group modulo torsion
j	1296134247276791/2137096192000	j-invariant
L	5.108574711313	L(r)(E,1)/r!
Ω	0.21703628753427	Real period
R	3.9229804758696	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	770b3 24640bs3 55440dw3 30800by3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 6160f3

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	-6	-2	6	0	-8	-4	12	4	-12	0	0	2	-8	-12	2	-14	-12	6	8

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Quadratic twists for elliptic curve 6160f3

-4	8	-3	5	-7	-11
770b3	24640bs3	55440dw3	30800by3	43120cu3	67760bs3

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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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