Properties

Label 5.3.am_cr_ajs_zh_abxw
Base Field $\F_{3}$
Dimension $5$
$p$-rank $0$
Does not contain a Jacobian

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Invariants

Base field:  $\F_{3}$
Dimension:  $5$
Weil polynomial:  $(1+3x^{2})(1-3x+3x^{2})^{4}$
Frobenius angles:  $\pm0.166666666667$, $\pm0.166666666667$, $\pm0.166666666667$, $\pm0.166666666667$, $\pm0.5$
Angle rank:  $0$ (numerical)

Newton polygon

This isogeny class is supersingular.

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

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
$A(\F_{q^r})$ 4 38416 17210368 4388797504 1316033637364 296196766695424 57994298718070348 12463412921879046400 2955063255987167847424 712025834662527967355536

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -8 4 28 100 352 1000 2512 6724 19684 58564

Decomposition

1.3.ad 4 $\times$ 1.3.a

Base change

This is a primitive isogeny class.