Properties

Label 2.4.ae_m
Base Field $\F_{2^2}$
Dimension $2$
$p$-rank $0$
Principally polarizable
Contains a Jacobian

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Invariants

Base field:  $\F_{2^2}$
Dimension:  $2$
Weil polynomial:  $(1-2x+4x^{2})^{2}$
Frobenius angles:  $\pm0.333333333333$, $\pm0.333333333333$
Angle rank:  $0$ (numerical)

Newton polygon

This isogeny class is supersingular.

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

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
$A(\F_{q^r})$ 9 441 6561 74529 986049 15752961 264290049 4328718849 69257922561 1101662259201

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 1 25 97 289 961 3841 16129 66049 264193 1050625

Decomposition

1.4.ac 2

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.a_ac