Properties

Label 4.3.ai_bk_aea_ig
Base Field $\F_{3}$
Dimension $4$
$p$-rank $4$
Does not contain a Jacobian

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Invariants

Base field:  $\F_{3}$
Dimension:  $4$
Weil polynomial:  $( 1 - 2 x + 3 x^{2} )^{4}$
Frobenius angles:  $\pm0.304086723985$, $\pm0.304086723985$, $\pm0.304086723985$, $\pm0.304086723985$
Angle rank:  $1$ (numerical)

Newton polygon

This isogeny class is ordinary.

$p$-rank:  $4$
Slopes:  $[0, 0, 0, 0, 1, 1, 1, 1]$

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 20736 2085136 84934656 3429742096 218889236736 19522293907216 1816019815366656 156005942621967376 12560354365595832576

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -4 18 68 138 236 546 1844 6426 20444 60978

Decomposition

1.3.ac 4

Base change

This is a primitive isogeny class.