Properties

 Label 2.3.a_f Base Field $\F_{3}$ Dimension $2$ $p$-rank $2$ Principally polarizable Contains a Jacobian

Invariants

 Base field: $\F_{3}$ Dimension: $2$ Weil polynomial: $( 1 - x + 3 x^{2} )( 1 + x + 3 x^{2} )$ Frobenius angles: $\pm0.406785250661$, $\pm0.593214749339$ 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 $A(\F_{q^r})$ 15 225 720 5625 58575 518400 4780455 44555625 387441360 3431030625

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 4 20 28 68 244 710 2188 6788 19684 58100

Decomposition

1.3.ab $\times$ 1.3.b

Base change

This is a primitive isogeny class.