Properties

Label 3.4.ag_v_abw
Base Field $\F_{2^2}$
Dimension $3$
$p$-rank $2$
Does not contain a Jacobian

Learn more about

Invariants

Base field:  $\F_{2^2}$
Dimension:  $3$
Weil polynomial:  $( 1 + 4 x^{2} )( 1 - 3 x + 4 x^{2} )^{2}$
Frobenius angles:  $\pm0.230053456163$, $\pm0.230053456163$, $\pm0.5$
Angle rank:  $1$ (numerical)

Newton polygon

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

Point counts

This isogeny class does not contain a Jacobian, and it is unknown whether it is principally polarizable.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 20 6400 355940 18662400 1199992100 72554809600 4352262413540 275475014553600 17877563727622820 1152531932448160000

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -1 23 83 287 1139 4319 16211 64127 260147 1048223

Decomposition

1.4.ad 2 $\times$ 1.4.a

Base change

This isogeny class is not primitive. It is a base change from the following isogeny classes over subfields of $\F_{2^2}$.

SubfieldPrimitive Model
$\F_{2}$3.2.c_ab_ag
$\F_{2}$3.2.ac_ab_g