Properties

Label 3.4.ag_w_abz
Base Field $\F_{2^2}$
Dimension $3$
$p$-rank $3$
Does not contain a Jacobian

Learn more about

Invariants

Base field:  $\F_{2^2}$
Dimension:  $3$
Weil polynomial:  $( 1 - 3 x + 4 x^{2} )( 1 - 3 x + 9 x^{2} - 12 x^{3} + 16 x^{4} )$
Frobenius angles:  $\pm0.230053456163$, $\pm0.272875599394$, $\pm0.469557725221$
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
$A(\F_{q^r})$ 22 7216 403744 18833760 1132606222 70451713024 4351625829958 276161419258560 17883137524955296 1154383439846479216

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -1 25 92 289 1079 4198 16211 64289 260228 1049905

Decomposition

1.4.ad $\times$ 2.4.ad_j

Base change

This is a primitive isogeny class.