Properties

 Label 3.2.ac_g_ai Base Field $\F_{2}$ Dimension $3$ $p$-rank $0$ Does not contain a Jacobian

Invariants

 Base field: $\F_{2}$ Dimension: $3$ Weil polynomial: $( 1 - 2 x + 2 x^{2} )( 1 + 2 x^{2} )^{2}$ Frobenius angles: $\pm0.25$, $\pm0.5$, $\pm0.5$ Angle rank: $0$ (numerical)

Newton polygon

This isogeny class is supersingular.

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

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 $A(\F_{q^r})$ 9 405 1053 2025 44649 426465 1880433 11390625 126584289 1215569025

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 1 13 13 9 41 97 113 161 481 1153

Decomposition

1.2.ac $\times$ 1.2.a 2

Base change

This is a primitive isogeny class.