Properties

Label 3.2.ad_g_ai
Base Field $\F_{2}$
Dimension $3$
$p$-rank $1$

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Invariants

Base field:  $\F_{2}$
Dimension:  $3$
Weil polynomial:  $( 1 + x + 2 x^{2} )( 1 - 2 x + 2 x^{2} )^{2}$
Frobenius angles:  $\pm0.25$, $\pm0.25$, $\pm0.615026728081$
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
$A(\F_{q^r})$ 4 200 676 10000 73964 236600 1481204 14580000 117531388 1017005000

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 0 8 12 32 60 56 84 224 444 968

Decomposition

1.2.ac 2 $\times$ 1.2.b

Base change

This is a primitive isogeny class.