Properties

Label 3.16.as_fx_abdt
Base Field $\F_{2^{4}}$
Dimension $3$
Ordinary Yes
$p$-rank $3$
Principally polarizable Yes
Contains a Jacobian No

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Invariants

Base field:  $\F_{2^{4}}$
Dimension:  $3$
L-polynomial:  $1 - 18 x + 153 x^{2} - 773 x^{3} + 2448 x^{4} - 4608 x^{5} + 4096 x^{6}$
Frobenius angles:  $\pm0.109406132665$, $\pm0.208302636123$, $\pm0.327763380346$
Angle rank:  $3$ (numerical)
Number field:  6.0.53163783.1
Galois group:  $A_4\times C_2$

This isogeny class is simple and geometrically simple.

Newton polygon

This isogeny class is ordinary.

$p$-rank:  $3$
Slopes:  $[0, 0, 0, 1, 1, 1]$

Point counts

This isogeny class is principally polarizable, but does not contain a Jacobian.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 1299 15714003 70610588649 284197314082827 1154536315694943789 4722792817067707241133 19343451997189727152706496 79230094696154960740871111307 324521185308632713376169547190031 1329229602188956485591291918661824813

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -1 239 4208 66167 1050044 16778732 268444322 4295072039 68720034011 1099512956564

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{4}}$
The endomorphism algebra of this simple isogeny class is 6.0.53163783.1.
All geometric endomorphisms are defined over $\F_{2^{4}}$.

Base change

This is a primitive isogeny class.

Twists

Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
3.16.s_fx_bdt$2$(not in LMFDB)