Properties

Label 2.4.ac_f
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:  $( 1 - 3 x + 4 x^{2} )( 1 + x + 4 x^{2} )$
Frobenius angles:  $\pm0.230053456163$, $\pm0.580430623255$
Angle rank:  $2$ (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
$A(\F_{q^r})$ 12 384 3996 69120 1175052 17006976 262951932 4280186880 68662073196 1096502123904

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 3 23 63 271 1143 4151 16047 65311 261927 1045703

Decomposition

1.4.ad $\times$ 1.4.b

Base change

This is a primitive isogeny class.