Properties

Label 3.13.au_gq_abfi
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:  $( 1 - 6 x + 13 x^{2} )( 1 - 7 x + 13 x^{2} )^{2}$
Frobenius angles:  $\pm0.0772104791556$, $\pm0.0772104791556$, $\pm0.187167041811$
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
$A(\F_{q^r})$ 392 3457440 10034898944 23181512860800 51232868046172232 112526703776073646080 247115398537287670388264 542828560531927606535692800 1192547229763648456436745832448 2620003957632192333290694379351200

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -6 114 2076 28418 371634 4829868 62761434 815772482 10604623308 137858929314

Decomposition

1.13.ah 2 $\times$ 1.13.ag

Base change

This is a primitive isogeny class.