Properties

Label 3.4.af_f_e
Base Field $\F_{2^2}$
Dimension $3$
$p$-rank $2$

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Invariants

Base field:  $\F_{2^2}$
Dimension:  $3$
Weil polynomial:  $( 1 - 2 x )^{2}( 1 - x - 3 x^{2} - 4 x^{3} + 16 x^{4} )$
Frobenius angles:  $0.0$, $0.0$, $\pm0.0862360434115$, $\pm0.752902710078$
Angle rank:  $1$ (numerical)

Newton polygon

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

Point counts

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 9 1539 142884 15736275 950187789 66849136704 4396680061461 278328896453475 18051316005094596 1152508529819247579

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 0 2 27 242 900 3983 16380 64802 262683 1048202

Decomposition

1.4.ae $\times$ 2.4.ab_ad

Base change

This is a primitive isogeny class.