Properties

Label 2.4.ab_ac
Base Field $\F_{2^2}$
Dimension $2$
$p$-rank $1$
Principally polarizable
Contains a Jacobian

Learn more about

Invariants

Base field:  $\F_{2^2}$
Dimension:  $2$
Weil polynomial:  $1 - x - 2 x^{2} - 4 x^{3} + 16 x^{4}$
Frobenius angles:  $\pm0.123737125646$, $\pm0.736024913457$
Angle rank:  $2$ (numerical)
Number field:  4.0.8405.1
Galois group:  $D_{4}$

This isogeny class is simple.

Newton polygon

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

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
$A(\F_{q^r})$ 10 200 3070 74000 1038550 17007800 276074830 4296884000 69074008390 1102005405000

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 4 12 46 288 1014 4152 16846 65568 263494 1050952

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.