Properties

Label 3.2.ad_i_am
Base Field $\F_{2}$
Dimension $3$
Ordinary No
$p$-rank $1$

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Invariants

Base field:  $\F_{2}$
Dimension:  $3$
Weil polynomial:  $( 1 - 2 x + 2 x^{2} )( 1 - x + 2 x^{2} )( 1 + 2 x^{2} )$
Frobenius angles:  $\pm0.25$, $\pm0.384973271919$, $\pm0.5$
Angle rank:  $1$ (numerical)

Newton polygon

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

Point counts

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 6 360 1638 3600 29766 294840 2069934 14580000 127818054 1080505800

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 0 12 18 16 30 72 126 224 486 1032

Decomposition

1.2.ac $\times$ 1.2.ab $\times$ 1.2.a

Base change

This is a primitive isogeny class.