Properties

Label 3.13.ap_dy_aqx
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:  $( 1 - x + 13 x^{2} )( 1 - 7 x + 13 x^{2} )^{2}$
Frobenius angles:  $\pm0.0772104791556$, $\pm0.0772104791556$, $\pm0.455715642762$
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
$A(\F_{q^r})$ 637 4213755 10125466624 22758933199275 50961221941086457 112500615380537180160 247131956265713730738709 542811441823314176232085275 1192537920497238107784957242368 2620019459632019140624088299414275

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -1 149 2096 27893 369659 4828748 62765639 815746757 10604540528 137859744989

Decomposition

1.13.ah 2 $\times$ 1.13.ab

Base change

This is a primitive isogeny class.