Properties

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

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Invariants

Base field:  $\F_{3}$
Dimension:  $5$
Weil polynomial:  $(1-3x+3x^{2})^{2}(1-4x+6x^{2}-7x^{3}+18x^{4}-36x^{5}+27x^{6})$
Frobenius angles:  $\pm0.045239890521$, $\pm0.166666666667$, $\pm0.166666666667$, $\pm0.239335307006$, $\pm0.691360448188$
Angle rank:  $3$ (numerical)

Newton polygon

$p$-rank:  $3$
Slopes:  $[0, 0, 0, 1/2, 1/2, 1/2, 1/2, 1, 1, 1]$

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
$A(\F_{q^r})$ 5 24255 8988560 5267337075 1082283492775 215575726544640 53420925605073745 12017202035056893675 2874085776613431618560 714887926089295297652775

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -6 0 15 116 304 765 2332 6484 19140 58800

Decomposition

1.3.ad 2 $\times$ 3.3.ae_g_ah

Base change

This is a primitive isogeny class.