Properties

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

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Invariants

Base field:  $\F_{2^2}$
Dimension:  $2$
Weil polynomial:  $(1-x+4x^{2})^{2}$
Frobenius angles:  $\pm0.419569376745$, $\pm0.419569376745$
Angle rank:  $1$ (numerical)

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
$A(\F_{q^r})$ 16 576 5776 57600 929296 16842816 276756496 4324377600 68311140496 1096007985216

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 3 31 87 223 903 4111 16887 65983 260583 1045231

Decomposition

1.4.ab 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_ab