Properties

Label 3.13.aq_el_atn
Base Field $\F_{13}$
Dimension $3$
$p$-rank $2$
Does not contain a Jacobian

Learn more about

Invariants

Base field:  $\F_{13}$
Dimension:  $3$
Weil polynomial:  $( 1 - 7 x + 13 x^{2} )( 1 - 9 x + 39 x^{2} - 117 x^{3} + 169 x^{4} )$
Frobenius angles:  $\pm0.0228181011636$, $\pm0.0772104791556$, $\pm0.419357734967$
Angle rank:  $3$ (numerical)

Newton polygon

$p$-rank:  $2$
Slopes:  $[0, 0, 1/2, 1/2, 1, 1]$

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
$A(\F_{q^r})$ 581 4087335 10141926704 22738764255375 50810670439501616 112355835810658614720 247078851740814348911033 542799313739293649787795375 1192510523761141254849914881328 2619984069431691288457929961900800

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -2 144 2101 27868 368563 4822533 62752156 815728532 10604296903 137857882839

Decomposition

1.13.ah $\times$ 2.13.aj_bn

Base change

This is a primitive isogeny class.