Properties

Label 3.2.ac_d_ae
Base Field $\F_{2}$
Dimension $3$
$p$-rank $2$

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Invariants

Base field:  $\F_{2}$
Dimension:  $3$
Weil polynomial:  $( 1 - x + 2 x^{2} )( 1 - x - 2 x^{3} + 4 x^{4} )$
Frobenius angles:  $\pm0.139386741866$, $\pm0.384973271919$, $\pm0.686170398078$
Angle rank:  $3$ (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
$A(\F_{q^r})$ 4 128 364 6656 30844 221312 3173132 21325824 133831516 1096565888

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 1 7 7 23 31 55 183 319 511 1047

Decomposition

1.2.ab $\times$ 2.2.ab_a

Base change

This is a primitive isogeny class.