Properties

Label 3.9.am_cu_akk
Base Field $\F_{3^2}$
Dimension $3$
$p$-rank $0$
Does not contain a Jacobian

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Invariants

Base field:  $\F_{3^2}$
Dimension:  $3$
Weil polynomial:  $(1-3x)^{2}(1-3x+9x^{2})^{2}$
Frobenius angles:  $0.0$, $0.0$, $\pm0.333333333333$, $\pm0.333333333333$
Angle rank:  $0$ (numerical)

Newton polygon

This isogeny class is supersingular.

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

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
$A(\F_{q^r})$ 196 529984 415507456 282428473600 202529728914436 148863517207035904 109219045860890723044 79766443076307650790400 58155645478328023283467264 42391158275215791732030243904

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -2 82 784 6562 58078 527068 4774222 43046722 387459856 3486784402

Decomposition

1.9.ag $\times$ 1.9.ad 2

Base change

This is a primitive isogeny class.