Properties

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

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Invariants

Base field:  $\F_{2^2}$
Dimension:  $2$
Weil polynomial:  $1-x+4x^{2}-4x^{3}+16x^{4}$
Frobenius angles:  $\pm0.278773483733$, $\pm0.627659203843$
Angle rank:  $2$ (numerical)
Number field:  4.0.2312.1
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
$A(\F_{q^r})$ 16 416 3952 74048 1132816 16132064 262967728 4303225472 68606478928 1099812538656

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 4 24 64 288 1104 3936 16048 65664 261712 1048864

Decomposition

This is a simple isogeny class.

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}$2.2.ab_a
$\F_{2}$2.2.b_a