Properties

Label 5.3.an_dc_alx_bgf_acmk
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:  $(1-3x+3x^{2})^{3}(1-4x+8x^{2}-12x^{3}+9x^{4})$
Frobenius angles:  $\pm0.0540867239847$, $\pm0.166666666667$, $\pm0.166666666667$, $\pm0.166666666667$, $\pm0.445913276015$
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
$A(\F_{q^r})$ 2 23324 13741952 3484512304 980835547102 256413830758400 57217773971730682 12492606163646988288 2911251624101322728576 709130876931861641930204

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -9 1 24 81 281 892 2483 6737 19392 58321

Decomposition

1.3.ad 3 $\times$ 2.3.ae_i

Base change

This is a primitive isogeny class.