Properties

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

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Invariants

Base field:  $\F_{3^2}$
Dimension:  $3$
Weil polynomial:  $1 - 12 x + 72 x^{2} - 269 x^{3} + 648 x^{4} - 972 x^{5} + 729 x^{6}$
Frobenius angles:  $\pm0.0639322448609$, $\pm0.291657634378$, $\pm0.365068394171$
Angle rank:  $3$ (numerical)
Number field:  6.0.6370731.1
Galois group:  The Galois group of this isogeny class is not in the database.

This isogeny class is simple.

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
$A(\F_{q^r})$ 197 532491 417860837 284525383539 203771469061997 149318100244576611 109320775574611200461 79778719574651271266979 58157069260879829537857088 42392499048133829713674232491

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -2 82 787 6610 58438 528685 4778674 43053346 387469336 3486894682

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.