Properties

Label 5.3.al_ch_aia_us_abow
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:  $(1-3x+3x^{2})(1-4x+8x^{2}-12x^{3}+9x^{4})^{2}$
Frobenius angles:  $\pm0.0540867239847$, $\pm0.0540867239847$, $\pm0.166666666667$, $\pm0.445913276015$, $\pm0.445913276015$
Angle rank:  $1$ (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
$A(\F_{q^r})$ 4 32368 10972528 1945705216 658181907004 221974241440000 54436404955943476 12063819633480695808 2868089541454266945424 715002677300852642155888

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -7 7 20 35 183 784 2373 6507 19100 58807

Decomposition

1.3.ad $\times$ 2.3.ae_i 2

Base change

This is a primitive isogeny class.