Properties

Label 2.9.ae_l
Base Field $\F_{3^2}$
Dimension $2$
$p$-rank $2$
Principally polarizable
Contains a Jacobian

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Invariants

Base field:  $\F_{3^2}$
Dimension:  $2$
Weil polynomial:  $1 - 4 x + 11 x^{2} - 36 x^{3} + 81 x^{4}$
Frobenius angles:  $\pm0.153401645225$, $\pm0.570422193164$
Angle rank:  $2$ (numerical)
Number field:  4.0.513040.2
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
$A(\F_{q^r})$ 53 7049 503924 42752185 3534063373 283368559376 22876228581133 1853558987367465 150114147085990004 12157375108436502329

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 6 88 690 6516 59846 533206 4782854 43059236 387470850 3486701128

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.