Properties

Label 2.81.abe_ow
Base Field $\F_{3^{4}}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{3^{4}}$
Dimension:  $2$
L-polynomial:  $( 1 - 16 x + 81 x^{2} )( 1 - 14 x + 81 x^{2} )$
Frobenius angles:  $\pm0.151478024726$, $\pm0.216346895939$
Angle rank:  $2$ (numerical)
Jacobians:  32

This isogeny class is not simple.

Newton polygon

This isogeny class is ordinary.

$p$-rank:  $2$
Slopes:  $[0, 0, 1, 1]$

Point counts

This isogeny class contains the Jacobians of 32 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 4488 42223104 282669611400 1853719921557504 12158361612293998728 79766908955767535040000 523347838028398318931175048 3433683839993696966739140542464 22528399478664295376291937646110600 147808829336564811862189637126571677184

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 52 6434 531892 43062974 3486984052 282431186018 22876801416052 1853020199483774 150094634855445172 12157665452659227554

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{3^{4}}$
The isogeny class factors as 1.81.aq $\times$ 1.81.ao and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:
All geometric endomorphisms are defined over $\F_{3^{4}}$.

Base change

This is a primitive isogeny class.

Twists

Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.81.ac_ack$2$(not in LMFDB)
2.81.c_ack$2$(not in LMFDB)
2.81.be_ow$2$(not in LMFDB)