Properties

Label 3.16.ar_fe_azf
Base Field $\F_{2^{4}}$
Dimension $3$
Ordinary Yes
$p$-rank $3$
Principally polarizable Yes

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Invariants

Base field:  $\F_{2^{4}}$
Dimension:  $3$
L-polynomial:  $1 - 17 x + 134 x^{2} - 655 x^{3} + 2144 x^{4} - 4352 x^{5} + 4096 x^{6}$
Frobenius angles:  $\pm0.0752779416406$, $\pm0.138403566317$, $\pm0.420922033917$
Angle rank:  $3$ (numerical)
Number field:  6.0.158451551.1
Galois group:  $S_4\times C_2$

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 it is unknown whether it contains a Jacobian.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 1351 15400049 67998430675 279372612310029 1151216629470707121 4724189513871257204075 19347691023493408167459784 79232186288355305856172468821 324519690235682278395932650164325 1329228700364569718584053444505095999

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 0 236 4053 65044 1047025 16783691 268503144 4295185420 68719717416 1099512210591

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{4}}$
The endomorphism algebra of this simple isogeny class is 6.0.158451551.1.
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.r_fe_zf$2$(not in LMFDB)