Properties

 Label 3.9.am_cq_ajm Base Field $\F_{3^2}$ Dimension $3$ $p$-rank $2$ Does not contain a Jacobian

Invariants

 Base field: $\F_{3^2}$ Dimension: $3$ Weil polynomial: $( 1 - 3 x )^{2}( 1 - 5 x + 9 x^{2} )( 1 - x + 9 x^{2} )$ Frobenius angles: $0.0$, $0.0$, $\pm0.186429498677$, $\pm0.446699620962$ Angle rank: $2$ (numerical)

Newton polygon

 $p$-rank: $2$ Slopes: $[0, 0, 1/2, 1/2, 1, 1]$

Point counts

This isogeny class does not contain a Jacobian, and it is unknown whether it is principally polarizable.

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 180 475200 378181440 274903200000 204591151026900 150287004912844800 109468657674159699060 79737216841532764800000 58134800970017038512947520 42388266689166895944175080000

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ -2 74 712 6386 58678 532124 4785142 43030946 387320968 3486546554

Decomposition

1.9.ag $\times$ 1.9.af $\times$ 1.9.ab

Base change

This is a primitive isogeny class.