Cremona's table of elliptic curves

27744 = 2⁵ · 3 · 17²

Field	Data	Notes
Atkin-Lehner	2- 3- 17+	Signs for the Atkin-Lehner involutions
Class	27744z	Isogeny class
Conductor	27744	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	9289699893268992 = 29 · 32 · 1710	Discriminant
Eigenvalues	2- 3- -2  0  4 -2 17+  0	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-55584,1965960]	[a1,a2,a3,a4,a6]
Generators	[-366:44506:27]	Generators of the group modulo torsion
j	1536800264/751689	j-invariant
L	6.1328435752529	L(r)(E,1)/r!
Ω	0.36433666745795	Real period
R	4.2082256076796	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	27744r3 55488cl3 83232j3 1632h3	Quadratic twists by: -4 8 -3 17

Hecke Eigenvalues for elliptic curve 27744z3

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

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Quadratic twists for elliptic curve 27744z3

-4	8	-3	17
27744r3	55488cl3	83232j3	1632h3

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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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