Properties

Label 5.2.ai_bh_ado_hj_alu
Base Field $\F_{2}$
Dimension $5$
$p$-rank $4$
Does not contain a Jacobian

Learn more about

Invariants

Base field:  $\F_{2}$
Dimension:  $5$
Weil polynomial:  $( 1 - 2 x + 2 x^{2} )( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )^{2}$
Frobenius angles:  $\pm0.123548644961$, $\pm0.123548644961$, $\pm0.25$, $\pm0.456881978294$, $\pm0.456881978294$
Angle rank:  $1$ (numerical)

Newton polygon

$p$-rank:  $4$
Slopes:  $[0, 0, 0, 0, 1/2, 1/2, 1, 1, 1, 1]$

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
$A(\F_{q^r})$ 1 1805 75088 731025 37864361 2168541440 54945865913 1100579337225 32857658578576 1271561917711025

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -5 7 13 11 35 109 191 259 481 1147

Decomposition

1.2.ac $\times$ 2.2.ad_f 2

Base change

This is a primitive isogeny class.