Properties

Label 3.13.at_gd_abcs
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:  $( 1 - 7 x + 13 x^{2} )( 1 - 6 x + 13 x^{2} )^{2}$
Frobenius angles:  $\pm0.0772104791556$, $\pm0.187167041811$, $\pm0.187167041811$
Angle rank:  $2$ (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
$A(\F_{q^r})$ 448 3763200 10449875968 23532042240000 51456798671174848 112633394568133017600 247142527839014863448512 542815143389447140638720000 1192521232758848936602628064256 2619980328648743183307244126080000

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -5 127 2164 28847 373255 4834444 62768323 815752319 10604392132 137857686007

Decomposition

1.13.ah $\times$ 1.13.ag 2

Base change

This is a primitive isogeny class.