Properties

Label 2.27.ao_dq
Base Field $\F_{3^3}$
Dimension $2$
$p$-rank $2$
Principally polarizable
Contains a Jacobian

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Invariants

Base field:  $\F_{3^3}$
Dimension:  $2$
Weil polynomial:  $( 1 - 10 x + 27 x^{2} )( 1 - 4 x + 27 x^{2} )$
Frobenius angles:  $\pm0.0877398280459$, $\pm0.374235869875$
Angle rank:  $2$ (numerical)

Newton polygon

This isogeny class is ordinary.

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

Point counts

This isogeny class contains a Jacobian, and hence is principally polarizable.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 432 525312 388788336 282088341504 205770439178352 150084962864833536 109420525804631796144 79766921119469941555200 58149787206719839230617904 42391159674417632728167293952

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 14 722 19754 530798 14340494 387395522 10460500106 282431229086 7625604068558 205891138890482

Decomposition

1.27.ak $\times$ 1.27.ae

Base change

This is a primitive isogeny class.