Properties

Label 3.2.ac_f_ai
Base Field $\F_{2}$
Dimension $3$
$p$-rank $2$
Does not contain a Jacobian

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Invariants

Base field:  $\F_{2}$
Dimension:  $3$
Weil polynomial:  $( 1 + 2 x^{2} )( 1 - 2 x + 3 x^{2} - 4 x^{3} + 4 x^{4} )$
Frobenius angles:  $\pm0.174442860055$, $\pm0.5$, $\pm0.546783656212$
Angle rank:  $2$ (numerical)

Newton polygon

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

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
$A(\F_{q^r})$ 6 252 558 2016 58146 492156 2069934 14716800 143731314 1101401532

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 1 11 7 7 51 107 127 223 547 1051

Decomposition

1.2.a $\times$ 2.2.ac_d

Base change

This is a primitive isogeny class.