Properties

Label 3.4.af_e_i
Base Field $\F_{2^2}$
Dimension $3$
$p$-rank $1$

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Invariants

Base field:  $\F_{2^2}$
Dimension:  $3$
Weil polynomial:  $( 1 - 2 x )^{4}( 1 + 3 x + 4 x^{2} )$
Frobenius angles:  $0.0$, $0.0$, $0.0$, $0.0$, $\pm0.769946543837$
Angle rank:  $1$ (numerical)

Newton polygon

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

Point counts

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 8 1296 134456 14580000 893968328 65280270384 4285102526552 275208376680000 17942256978019304 1147110230217915216

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 0 0 24 224 840 3888 15960 64064 261096 1043280

Decomposition

1.4.ae 2 $\times$ 1.4.d

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}$3.2.ab_ac_e
$\F_{2}$3.2.b_ac_ae