Properties

Label 3.4.al_ca_afg
Base Field $\F_{2^2}$
Dimension $3$
$p$-rank $1$
Does not contain a Jacobian

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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:  $0.0$, $0.0$, $0.0$, $0.0$, $\pm0.230053456163$
Angle rank:  $1$ (numerical)

Newton polygon

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

Point counts

This isogeny class does not contain a Jacobian, and it is unknown whether it is principally polarizable.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 2 1296 177674 14580000 999249722 65280270384 4239837359018 275208376680000 17806024993090586 1147110230217915216

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -6 0 42 224 954 3888 15786 64064 259098 1043280

Decomposition

1.4.ae 2 $\times$ 1.4.ad

Base change

This is a primitive isogeny class.