Properties

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

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Invariants

Base field:  $\F_{2^2}$
Dimension:  $3$
Weil polynomial:  $( 1 - 3 x + 4 x^{2} )( 1 - 3 x + 6 x^{2} - 12 x^{3} + 16 x^{4} )$
Frobenius angles:  $\pm0.15043295046$, $\pm0.230053456163$, $\pm0.544835058382$
Angle rank:  $3$ (numerical)

Newton polygon

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

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
$A(\F_{q^r})$ 16 4864 270544 17685504 1235306416 73116139264 4385031530896 280368224169984 18044032744823152 1151937048586956544

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -1 19 65 271 1169 4351 16337 65279 262577 1047679

Decomposition

1.4.ad $\times$ 2.4.ad_g

Base change

This is a primitive isogeny class.