Properties

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

Learn more about

Invariants

Base field:  $\F_{2}$
Dimension:  $3$
Weil polynomial:  $( 1 - x + 2 x^{2} )( 1 - 2 x + 2 x^{2} - 4 x^{3} + 4 x^{4} )$
Frobenius angles:  $\pm0.0833333333333$, $\pm0.384973271919$, $\pm0.583333333333$
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
$A(\F_{q^r})$ 2 104 350 2704 29062 236600 2051758 21464352 153858950 1014031304

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 0 8 6 8 30 56 126 320 582 968

Decomposition

1.2.ab $\times$ 2.2.ac_c

Base change

This is a primitive isogeny class.