Properties

Label 3.4.ak_bt_aem
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:  $( 1 - 2 x )^{2}( 1 - 3 x + 4 x^{2} )^{2}$
Frobenius angles:  $0.0$, $0.0$, $\pm0.230053456163$, $\pm0.230053456163$
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
$A(\F_{q^r})$ 4 2304 268324 18662400 1125065764 68158589184 4284262463716 275475014553600 17807729760707236 1148038634844059904

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -5 7 67 287 1075 4063 15955 64127 259123 1044127

Decomposition

1.4.ae $\times$ 1.4.ad 2

Base change

This is a primitive isogeny class.