Properties

Label 5.3.ak_bv_afj_lr_avj
Base Field $\F_{3}$
Dimension $5$
$p$-rank $3$
Does not contain a Jacobian

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Invariants

Base field:  $\F_{3}$
Dimension:  $5$
Weil polynomial:  $(1-3x+3x^{2})^{2}(1-4x+8x^{2}-13x^{3}+24x^{4}-36x^{5}+27x^{6})$
Frobenius angles:  $\pm0.102762435325$, $\pm0.166666666667$, $\pm0.166666666667$, $\pm0.278353759721$, $\pm0.64326535244$
Angle rank:  $3$ (numerical)

Newton polygon

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

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 38759 11464432 5430174659 1229650350257 220397560264448 53076707805199099 12768830646189408427 2963011331031393467392 721245798565095685030919

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -6 4 21 116 334 781 2318 6884 19740 59324

Decomposition

1.3.ad 2 $\times$ 3.3.ae_i_an

Base change

This is a primitive isogeny class.