Properties

Label 3.4.ag_y_ace
Base Field $\F_{2^2}$
Dimension $3$
$p$-rank $0$
Does not contain a Jacobian

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Invariants

Base field:  $\F_{2^2}$
Dimension:  $3$
Weil polynomial:  $( 1 - 2 x + 4 x^{2} )^{3}$
Frobenius angles:  $\pm0.333333333333$, $\pm0.333333333333$, $\pm0.333333333333$
Angle rank:  $0$ (numerical)

Newton polygon

This isogeny class is supersingular.

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

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
$A(\F_{q^r})$ 27 9261 531441 20346417 979146657 62523502209 4296563326593 284799399232257 18226538222455809 1156305808919628801

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -1 29 113 305 929 3713 16001 66305 265217 1051649

Decomposition

1.4.ac 3

Base change

This is a primitive isogeny class.