Properties

Label 3.4.am_ci_age
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:  $( 1 - 2 x )^{6}$
Frobenius angles:  $0.0$, $0.0$, $0.0$, $0.0$, $0.0$, $0.0$
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
$A(\F_{q^r})$ 1 729 117649 11390625 887503681 62523502209 4195872914689 274941996890625 17804320388674561 1146182576381093889

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -7 -7 17 161 833 3713 15617 64001 259073 1042433

Decomposition

1.4.ae 3

Base change

This is a primitive isogeny class.