Properties

Label 2.4.ab_g
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:  $( 1 - 2 x + 4 x^{2} )( 1 + x + 4 x^{2} )$
Frobenius angles:  $\pm0.333333333333$, $\pm0.580430623255$
Angle rank:  $1$ (numerical)

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
$A(\F_{q^r})$ 18 504 4374 65520 1078398 16288776 262290438 4326547680 69193972494 1098831485304

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 4 28 70 256 1054 3976 16006 66016 263950 1047928

Decomposition

1.4.ac $\times$ 1.4.b

Base change

This is a primitive isogeny class.