Properties

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

Learn more about

Invariants

Base field:  $\F_{13}$
Dimension:  $3$
Weil polynomial:  $( 1 - 6 x + 13 x^{2} )( 1 - 9 x + 42 x^{2} - 117 x^{3} + 169 x^{4} )$
Frobenius angles:  $\pm0.136139978944$, $\pm0.187167041811$, $\pm0.390198274089$
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
$A(\F_{q^r})$ 688 4650880 10964218432 23480618803200 51274688479675888 112587197950684487680 247202755971073843853488 542872893304061401979289600 1192537349150551687055542497088 2619975166112142019158876065814400

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -1 163 2270 28783 371939 4832464 62783615 815839103 10604535446 137857414363

Decomposition

1.13.ag $\times$ 2.13.aj_bq

Base change

This is a primitive isogeny class.