Cremona's table of elliptic curves

27720 = 2³ · 3² · 5 · 7 · 11

Field	Data	Notes
Atkin-Lehner	2- 3- 5+ 7- 11+	Signs for the Atkin-Lehner involutions
Class	27720bk	Isogeny class
Conductor	27720	Conductor
∏ cp	256	Product of Tamagawa factors cp
Δ	1355454777600 = 28 · 36 · 52 · 74 · 112	Discriminant
Eigenvalues	2- 3- 5+ 7- 11+ -6 -6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-6543,195858]	[a1,a2,a3,a4,a6]
Generators	[61:-154:1] [-71:550:1]	Generators of the group modulo torsion
j	165991931856/7263025	j-invariant
L	7.8171122572528	L(r)(E,1)/r!
Ω	0.84741491831934	Real period
R	0.5765410845579	Regulator
r	2	Rank of the group of rational points
S	0.99999999999986	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	55440o2 3080b2	Quadratic twists by: -4 -3

Hecke Eigenvalues for elliptic curve 27720bk2

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
-	-	+	-	+	-6	-6	-4	-4	-6	0	-10	-10	4	-12	-6	4	14	-8	-16	-2	0	-12	6	18

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Quadratic twists for elliptic curve 27720bk2

-4	-3
55440o2	3080b2

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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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