Properties

Label 3.13.as_fp_azv
Base Field $\F_{13}$
Dimension $3$
$p$-rank $3$
Does not contain a Jacobian

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Invariants

Base field:  $\F_{13}$
Dimension:  $3$
Weil polynomial:  $( 1 - 7 x + 13 x^{2} )( 1 - 11 x + 55 x^{2} - 143 x^{3} + 169 x^{4} )$
Frobenius angles:  $\pm0.0772104791556$, $\pm0.129998747777$, $\pm0.292104599859$
Angle rank:  $3$ (numerical)

Newton polygon

This isogeny class is ordinary.

$p$-rank:  $3$
Slopes:  $[0, 0, 0, 1, 1, 1]$

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
$A(\F_{q^r})$ 497 3955623 10532193392 23398526640111 51224412916463472 112449530624823290304 247070573660859256322357 542833575266085419511276207 1192575668211041284187628658544 2620028268159512012487928792781568

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -4 136 2183 28684 371571 4826557 62750054 815780020 10604876189 137860208471

Decomposition

1.13.ah $\times$ 2.13.al_cd

Base change

This is a primitive isogeny class.