Properties

 Label 2.3.ad_h Base Field $\F_{3}$ Dimension $2$ Ordinary No $p$-rank $2$ Principally polarizable Yes Contains a Jacobian Yes

Invariants

 Base field: $\F_{3}$ Dimension: $2$ Weil polynomial: $1 - 3 x + 7 x^{2} - 9 x^{3} + 9 x^{4}$ Frobenius angles: $\pm0.227267020856$, $\pm0.464830336654$ Angle rank: $2$ (numerical) Number field: 4.0.1525.1 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.

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 5 145 1055 6525 62000 581305 4870955 41505525 377427305 3480928000

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 1 15 37 83 256 795 2227 6323 19171 58950

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.