Properties

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

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Invariants

Base field:  $\F_{3}$
Dimension:  $4$
Weil polynomial:  $( 1 - 3 x + 3 x^{2} )( 1 - 5 x + 13 x^{2} - 25 x^{3} + 39 x^{4} - 45 x^{5} + 27 x^{6} )$
Frobenius angles:  $\pm0.0714477711956$, $\pm0.166666666667$, $\pm0.27207177608$, $\pm0.560185743604$
Angle rank:  $3$ (numerical)

Newton polygon

$p$-rank:  $3$
Slopes:  $[0, 0, 0, 1/2, 1/2, 1, 1, 1]$

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
$A(\F_{q^r})$ 5 5425 457940 44078125 4326589525 300106399600 21852060841280 1845111414453125 152838760198077380 12202985346955860625

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -4 8 23 84 296 773 2089 6532 20039 59268

Decomposition

1.3.ad $\times$ 3.3.af_n_az

Base change

This is a primitive isogeny class.