Properties

Label 5.3.al_cg_ahn_sj_abji
Base Field $\F_{3}$
Dimension $5$
$p$-rank $2$
Does not contain a Jacobian

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Invariants

Base field:  $\F_{3}$
Dimension:  $5$
Weil polynomial:  $(1-3x+3x^{2})^{3}(1-2x+4x^{2}-6x^{3}+9x^{4})$
Frobenius angles:  $\pm0.166666666667$, $\pm0.166666666667$, $\pm0.166666666667$, $\pm0.210767374595$, $\pm0.567777800232$
Angle rank:  $2$ (numerical)

Newton polygon

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

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
$A(\F_{q^r})$ 6 45276 15410304 5172511344 1483254534786 275365612634112 53718004017998718 12491705600918928384 2954227408873043442048 700557230094300884223996

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -7 5 26 113 383 944 2345 6737 19682 57605

Decomposition

1.3.ad 3 $\times$ 2.3.ac_e

Base change

This is a primitive isogeny class.