Properties

Label 3.4.ag_m_aq
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:  $( 1 - 2 x )^{4}( 1 + 2 x + 4 x^{2} )$
Frobenius angles:  $0.0$, $0.0$, $0.0$, $0.0$, $\pm0.666666666667$
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
$A(\F_{q^r})$ 7 1701 117649 13820625 976161697 62523502209 4295768456833 278189293370625 17804320388674561 1149547101276861441

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -1 5 17 209 929 3713 16001 64769 259073 1045505

Decomposition

1.4.ae 2 $\times$ 1.4.c

Base change

This is a primitive isogeny class.