Properties

Label 5.3.al_ci_aih_vp_abqs
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:  $(1-x+3x^{2})(1-3x+3x^{2})^{2}(1-4x+8x^{2}-12x^{3}+9x^{4})$
Frobenius angles:  $\pm0.0540867239847$, $\pm0.166666666667$, $\pm0.166666666667$, $\pm0.406785250661$, $\pm0.445913276015$
Angle rank:  $2$ (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
$A(\F_{q^r})$ 6 49980 17668224 2871850800 770915024106 235482089472000 57268208325165438 12552784305636556800 2891137306844780364672 706333278628119027939900

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -7 9 32 65 223 828 2485 6769 19256 58089

Decomposition

1.3.ad 2 $\times$ 1.3.ab $\times$ 2.3.ae_i

Base change

This is a primitive isogeny class.