Properties

Label 5.3.al_cj_ain_wh_absc
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:  $(1-2x+3x^{2})(1-3x+3x^{2})^{2}(1-3x+7x^{2}-9x^{3}+9x^{4})$
Frobenius angles:  $\pm0.166666666667$, $\pm0.166666666667$, $\pm0.227267020856$, $\pm0.304086723985$, $\pm0.464830336654$
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
$A(\F_{q^r})$ 10 85260 31430560 5187218400 1101908764000 244394982558720 52712767854495010 11956788913150972800 2906332605830394821920 716644154693490866304000

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -7 11 47 115 308 857 2303 6451 19361 58946

Decomposition

1.3.ad 2 $\times$ 1.3.ac $\times$ 2.3.ad_h

Base change

This is a primitive isogeny class.