Properties

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

Learn more about

Invariants

Base field:  $\F_{3^3}$
Dimension:  $2$
Weil polynomial:  $1 - 14 x + 98 x^{2} - 378 x^{3} + 729 x^{4}$
Frobenius angles:  $\pm0.151580709202$, $\pm0.348419290798$
Angle rank:  $1$ (numerical)
Number field:  \(\Q(i, \sqrt{5})\)
Galois group:  $V_4$

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
$A(\F_{q^r})$ 436 531920 392133604 282938886400 205894948939556 150094634644128080 109420681608829356404 79766914395414351974400 58149792769259473116882196 42391158275216613267267698000

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 14 730 19922 532398 14349174 387420490 10460515002 282431205278 7625604798014 205891132094650

Decomposition

This is a simple isogeny class.

Base change

This isogeny class is not primitive. It is a base change from the following isogeny classes over subfields of $\F_{3^3}$.

SubfieldPrimitive Model
$\F_{3}$2.3.ac_c