Properties

 Label 2.27.ao_dw 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: $1 - 14 x + 100 x^{2} - 378 x^{3} + 729 x^{4}$ 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.

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 438 535236 393809742 283351797456 205945173103758 150093985274882532 109419197235921297078 79766614522397377655808 58149760872397683809810214 42391156599345582179325862116

 $r$ 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.