Properties

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

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Invariants

Base field:  $\F_{2}$
Dimension:  $3$
Weil polynomial:  $1 - 2 x + x^{2} + 2 x^{4} - 8 x^{5} + 8 x^{6}$
Frobenius angles:  $\pm0.069353354755$, $\pm0.339907131295$, $\pm0.77055377654$
Angle rank:  $2$ (numerical)
Number field:  6.0.2580992.1
Galois group:  $D_{6}$

This isogeny class is simple.

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
$A(\F_{q^r})$ 2 44 386 5984 16742 212300 2105602 16683392 164730518 1094290604

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 1 3 7 23 11 51 127 255 619 1043

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.