Properties

Label 2.4.ad_j
Base Field $\F_{2^2}$
Dimension $2$
$p$-rank $2$
Principally polarizable
Contains a Jacobian

Learn more about

Invariants

Base field:  $\F_{2^2}$
Dimension:  $2$
Weil polynomial:  $1 - 3 x + 9 x^{2} - 12 x^{3} + 16 x^{4}$
Frobenius angles:  $\pm0.272875599394$, $\pm0.469557725221$
Angle rank:  $2$ (numerical)
Number field:  4.0.3625.1
Galois group:  $D_{4}$

This isogeny class is simple.

Newton polygon

This isogeny class is ordinary.

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

Point counts

This isogeny class contains a Jacobian, and hence is principally polarizable.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 11 451 5456 65395 1046771 17000896 267003671 4242892995 68479461776 1102167168091

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 2 26 83 258 1022 4151 16298 64738 261227 1051106

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.