Properties

Label 3.9.am_cs_ajx
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:  $1 - 12 x + 70 x^{2} - 257 x^{3} + 630 x^{4} - 972 x^{5} + 729 x^{6}$
Frobenius angles:  $\pm0.0749946225172$, $\pm0.217193452972$, $\pm0.419068678586$
Angle rank:  $3$ (numerical)
Number field:  6.0.62548403.1
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
$A(\F_{q^r})$ 189 504819 398983725 281059492707 205254129344229 150288301794211875 109518389670415966821 79768313700270755940387 58142522905613776008993600 42389756217641606131157555259

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -2 78 751 6530 58868 532125 4787312 43047730 387372424 3486669078

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.