Properties

Label 4.3.ai_bi_ads_hm
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:  $( 1 - 2 x + 3 x^{2} )^{2}( 1 - 4 x + 8 x^{2} - 12 x^{3} + 9 x^{4} )$
Frobenius angles:  $\pm0.0540867239847$, $\pm0.304086723985$, $\pm0.304086723985$, $\pm0.445913276015$
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
$A(\F_{q^r})$ 8 9792 903944 42614784 2886151048 248946177600 21641775795592 1816019815366656 150768372127835144 12357774548336619072

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -4 14 44 82 196 638 2068 6426 19772 60014

Decomposition

1.3.ac 2 $\times$ 2.3.ae_i

Base change

This is a primitive isogeny class.