Properties

Label 2.27.ao_dw
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:  $1 - 14 x + 100 x^{2} - 378 x^{3} + 729 x^{4}$
Frobenius angles:  $\pm0.182412883256$, $\pm0.33078814005$
Angle rank:  $2$ (numerical)
Number field:  4.0.366912.2
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
$A(\F_{q^r})$ 438 535236 393809742 283351797456 205945173103758 150093985274882532 109419197235921297078 79766614522397377655808 58149760872397683809810214 42391156599345582179325862116

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 14 734 20006 533174 14352674 387418814 10460373098 282430143518 7625600615150 205891123955054

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.