Properties

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

Invariants

 Base field: $\F_{3^3}$ Dimension: $2$ Weil polynomial: $( 1 - 8 x + 27 x^{2} )^{2}$ Frobenius angles: $\pm0.220355751984$, $\pm0.220355751984$ Angle rank: $1$ (numerical)

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.

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 400 518400 392832400 283875840000 206097607210000 150110807438649600 109418419607862960400 79766001763821527040000 58149652889573220433248400 42391148793086358941369760000

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 12 710 19956 534158 14363292 387462230 10460298756 282427973918 7625586454572 205891086040550

1.27.ai 2

Base change

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

 Subfield Primitive Model $\F_{3}$ 2.3.c_h $\F_{3}$ 2.3.ab_ac