Properties

Label 4.3.ah_z_acj_en
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:  $( 1 - 3 x + 3 x^{2} )( 1 - 4 x + 10 x^{2} - 19 x^{3} + 30 x^{4} - 36 x^{5} + 27 x^{6} )$
Frobenius angles:  $\pm0.125412673718$, $\pm0.166666666667$, $\pm0.335294135736$, $\pm0.5848234043$
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
$A(\F_{q^r})$ 9 8001 531468 49614201 4332861549 296714332656 23230256952681 1974715900036425 155745282861778176 12133301575821043401

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -3 11 27 91 297 767 2223 6979 20412 58931

Decomposition

1.3.ad $\times$ 3.3.ae_k_at

Base change

This is a primitive isogeny class.