Properties

Label 3.13.aq_er_avc
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:  $( 1 - 6 x + 13 x^{2} )( 1 - 10 x + 48 x^{2} - 130 x^{3} + 169 x^{4} )$
Frobenius angles:  $\pm0.116678169037$, $\pm0.187167041811$, $\pm0.350288405554$
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
$A(\F_{q^r})$ 624 4467840 10940759856 23550520780800 51274742338460784 112513219458313265280 247142536546851714945072 542869186009725389360332800 1192564031792866668133252649712 2619994753948078634931259038211200

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -2 156 2266 28868 371938 4829292 62768326 815833532 10604772718 137858445036

Decomposition

1.13.ag $\times$ 2.13.ak_bw

Base change

This is a primitive isogeny class.