Properties

Label 2.27.as_fe
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:  $( 1 - 10 x + 27 x^{2} )( 1 - 8 x + 27 x^{2} )$
Frobenius angles:  $\pm0.0877398280459$, $\pm0.220355751984$
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
$A(\F_{q^r})$ 360 492480 386371080 282801715200 205973541793800 150103986920948160 109419455535786063720 79766400327280865280000 58149728196243978651094440 42391159009889917457517566400

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 10 674 19630 532142 14354650 387444626 10460397790 282429385118 7625596330090 205891135662914

Decomposition

1.27.ak $\times$ 1.27.ai

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.d_i