Properties

Label 2.27.aq_eo
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:  $( 1 - 8 x + 27 x^{2} )^{2}$
Frobenius angles:  $\pm0.220355751984$, $\pm0.220355751984$
Angle rank:  $1$ (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
$A(\F_{q^r})$ 400 518400 392832400 283875840000 206097607210000 150110807438649600 109418419607862960400 79766001763821527040000 58149652889573220433248400 42391148793086358941369760000

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 12 710 19956 534158 14363292 387462230 10460298756 282427973918 7625586454572 205891086040550

Decomposition

1.27.ai 2

Base change

This isogeny class is not primitive. It is a base change from the following isogeny classes over subfields of $\F_{3^3}$.

SubfieldPrimitive Model
$\F_{3}$2.3.c_h
$\F_{3}$2.3.ab_ac