Properties

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

Learn more about

Invariants

Base field:  $\F_{2}$
Dimension:  $3$
Weil polynomial:  $1 - 3 x + 5 x^{2} - 7 x^{3} + 10 x^{4} - 12 x^{5} + 8 x^{6}$
Frobenius angles:  $\pm0.105278500939$, $\pm0.316838792568$, $\pm0.641249159631$
Angle rank:  $3$ (numerical)
Number field:  6.0.679024.1
Galois group:  $S_4\times C_2$

This isogeny class is simple.

Newton polygon

This isogeny class is ordinary.

$p$-rank:  $3$
Slopes:  $[0, 0, 0, 1, 1, 1]$

Point counts

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 2 92 302 6256 42842 180596 2062538 21270400 147805142 1184409932

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 0 6 6 22 40 42 126 318 564 1126

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.