Properties

Label 5.3.al_cd_agm_of_azz
Base Field $\F_{3}$
Dimension $5$
$p$-rank $2$
Does not contain a Jacobian

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Invariants

Base field:  $\F_{3}$
Dimension:  $5$
Weil polynomial:  $(1-3x+3x^{2})^{3}(1-2x+x^{2}-6x^{3}+9x^{4})$
Frobenius angles:  $\pm0.0292466093486$, $\pm0.166666666667$, $\pm0.166666666667$, $\pm0.166666666667$, $\pm0.637420057318$
Angle rank:  $1$ (numerical)

Newton polygon

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

Point counts

This isogeny class does not contain a Jacobian, and it is unknown whether it is principally polarizable.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 3 19551 7112448 4166494059 1160774149053 225455270068224 53735631599342199 12683049676413773475 2898291028811761062144 703354545982222577820111

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -7 -1 8 95 323 800 2345 6839 19304 57839

Decomposition

1.3.ad 3 $\times$ 2.3.ac_b

Base change

This is a primitive isogeny class.