Properties

Label 5.3.al_ch_ahw_tt_abml
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:  $(1-3x+3x^{2})^{3}(1-2x+5x^{2}-6x^{3}+9x^{4})$
Frobenius angles:  $\pm0.166666666667$, $\pm0.166666666667$, $\pm0.166666666667$, $\pm0.254551732336$, $\pm0.538152604671$
Angle rank:  $2$ (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
$A(\F_{q^r})$ 7 55223 19054336 4974322171 1376596978337 269372824813568 52353414280000883 12138856505398324611 2966149666575644571904 712088368727173824104663

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -7 7 32 111 363 928 2289 6551 19760 58567

Decomposition

1.3.ad 3 $\times$ 2.3.ac_f

Base change

This is a primitive isogeny class.