Properties

Label 5.3.ak_bx_agc_or_abce
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:  $(1-3x+3x^{2})^{2}(1-4x+10x^{2}-20x^{3}+30x^{4}-36x^{5}+27x^{6})$
Frobenius angles:  $\pm0.0844416807585$, $\pm0.166666666667$, $\pm0.166666666667$, $\pm0.360432408976$, $\pm0.575465777728$
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
$A(\F_{q^r})$ 8 50176 13121024 3697168384 1036176718888 226476012077056 52415886206779096 13023712682309009408 3052799073160079161856 711112415711367293510656

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -6 8 24 84 294 800 2290 7012 20328 58488

Decomposition

1.3.ad 2 $\times$ 3.3.ae_k_au

Base change

This is a primitive isogeny class.