Properties

Label 5.3.ak_bx_agf_pk_abea
Base Field $\F_{3}$
Dimension $5$
$p$-rank $4$
Does not contain a Jacobian

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Invariants

Base field:  $\F_{3}$
Dimension:  $5$
Weil polynomial:  $(1-3x+3x^{2})(1-4x+8x^{2}-12x^{3}+9x^{4})(1-3x+5x^{2}-9x^{3}+9x^{4})$
Frobenius angles:  $\pm0.0540867239847$, $\pm0.0975263560046$, $\pm0.166666666667$, $\pm0.445913276015$, $\pm0.527857038681$
Angle rank:  $3$ (numerical)

Newton polygon

$p$-rank:  $4$
Slopes:  $[0, 0, 0, 0, 1/2, 1/2, 1, 1, 1, 1]$

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
$A(\F_{q^r})$ 6 38556 9622872 2079093744 834019393056 241162644340800 53102206257069738 12187289058301034496 2979526135323074630328 724672736650145506599936

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -6 8 15 40 239 845 2318 6576 19851 59603

Decomposition

1.3.ad $\times$ 2.3.ae_i $\times$ 2.3.ad_f

Base change

This is a primitive isogeny class.