Properties

Label 3.3.ag_v_abs
Base Field $\F_{3}$
Dimension $3$
$p$-rank $3$
Does not contain a Jacobian

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Invariants

Base field:  $\F_{3}$
Dimension:  $3$
Weil polynomial:  $( 1 - 2 x + 3 x^{2} )^{3}$
Frobenius angles:  $\pm0.304086723985$, $\pm0.304086723985$, $\pm0.304086723985$
Angle rank:  $1$ (numerical)

Newton polygon

This isogeny class is ordinary.

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

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
$A(\F_{q^r})$ 8 1728 54872 884736 14172488 320013504 9287485208 278189309952 7849750559624 210984921816768

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -2 16 58 124 238 592 1930 6460 20254 60496

Decomposition

1.3.ac 3

Base change

This is a primitive isogeny class.