Properties

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

Learn more about

Invariants

Base field:  $\F_{3^3}$
Dimension:  $2$
Weil polynomial:  $1 - 15 x + 103 x^{2} - 405 x^{3} + 729 x^{4}$
Frobenius angles:  $\pm0.0625058430386$, $\pm0.346918783446$
Angle rank:  $2$ (numerical)
Number field:  4.0.293509.1
Galois group:  $D_4$

This isogeny class is simple.

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
$A(\F_{q^r})$ 413 517489 388280711 282150009981 205757737375568 150074047958286361 109418094950958150707 79766671601625355642869 58149784272576394508220929 42391161108409570152526561024

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 13 711 19729 530915 14339608 387367347 10460267719 282430345619 7625603683783 205891145855286

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.