Properties

Label 5.3.an_de_amp_biz_acsq
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:  $(1-2x+3x^{2})^{2}(1-3x+3x^{2})^{3}$
Frobenius angles:  $\pm0.166666666667$, $\pm0.166666666667$, $\pm0.166666666667$, $\pm0.304086723985$, $\pm0.304086723985$
Angle rank:  $1$ (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
$A(\F_{q^r})$ 4 49392 31698688 6944910336 1165570654204 225455270068224 51614165618530036 12492606163646988288 3012386135220532021504 720755591632702229851632

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -9 5 48 137 321 800 2259 6737 20064 59285

Decomposition

1.3.ad 3 $\times$ 1.3.ac 2

Base change

This is a primitive isogeny class.