Properties

Label 2.27.am_cv
Base Field $\F_{3^3}$
Dimension $2$
$p$-rank $2$
Principally polarizable
Contains a Jacobian

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Invariants

Base field:  $\F_{3^3}$
Dimension:  $2$
Weil polynomial:  $1 - 12 x + 73 x^{2} - 324 x^{3} + 729 x^{4}$
Frobenius angles:  $\pm0.0726085987131$, $\pm0.442194681338$
Angle rank:  $2$ (numerical)
Number field:  4.0.166753.1
Galois group:  $D_4$

This isogeny class is simple.

Newton polygon

This isogeny class is ordinary.

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

Point counts

This isogeny class contains a Jacobian, and hence is principally polarizable.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 467 531913 386010992 281378253609 205760145436187 150098632557604096 109421089048455372851 79766483187481857166473 58149714501611151259711088 42391160693482363976220749113

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 16 732 19612 529460 14339776 387430806 10460553952 282429678500 7625594534212 205891143840012

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.