Properties

Label 5.2.ak_by_age_nw_awu
Base Field $\F_{2}$
Dimension $5$
$p$-rank $0$
Does not contain a Jacobian

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Invariants

Base field:  $\F_{2}$
Dimension:  $5$
Weil polynomial:  $( 1 - 2 x + 2 x^{2} )^{5}$
Frobenius angles:  $\pm0.25$, $\pm0.25$, $\pm0.25$, $\pm0.25$, $\pm0.25$
Angle rank:  $0$ (numerical)

Newton polygon

This isogeny class is supersingular.

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

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
$A(\F_{q^r})$ 1 3125 371293 9765625 115856201 1160290625 18424351793 576650390625 25746925826401 1131408212890625

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -7 5 29 57 73 65 49 97 353 1025

Decomposition

1.2.ac 5

Base change

This is a primitive isogeny class.