Properties

Label 4.3.ai_bh_adn_hb
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:  $( 1 - 3 x + 3 x^{2} )( 1 - 5 x + 15 x^{2} - 31 x^{3} + 45 x^{4} - 45 x^{5} + 27 x^{6} )$
Frobenius angles:  $\pm0.11329654039$, $\pm0.166666666667$, $\pm0.35182386554$, $\pm0.481790494592$
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
$A(\F_{q^r})$ 7 8281 732844 40585181 3533486887 315571420528 24860761811648 1917568997154629 153059630035416076 12278172330073214201

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -4 12 35 76 246 813 2369 6788 20069 59632

Decomposition

1.3.ad $\times$ 3.3.af_p_abf

Base change

This is a primitive isogeny class.