Properties

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

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Invariants

Base field:  $\F_{2}$
Dimension:  $3$
Weil polynomial:  $( 1 - 2 x + 2 x^{2} )( 1 - x - x^{2} - 2 x^{3} + 4 x^{4} )$
Frobenius angles:  $\pm0.0516399385854$, $\pm0.25$, $\pm0.718306605252$
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
$A(\F_{q^r})$ 1 35 208 6475 30791 203840 2045639 13111875 124128784 1136957675

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 0 2 3 26 30 47 126 194 471 1082

Decomposition

1.2.ac $\times$ 2.2.ab_ab

Base change

This is a primitive isogeny class.