# Properties

 Label 3.4.ai_bc_acm Base Field $\F_{2^2}$ Dimension $3$ $p$-rank $0$ Does not contain a Jacobian

## Invariants

 Base field: $\F_{2^2}$ Dimension: $3$ Weil polynomial: $( 1 - 2 x )^{4}( 1 + 4 x^{2} )$ Frobenius angles: $0.0$, $0.0$, $0.0$, $0.0$, $\pm0.5$ 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 $A(\F_{q^r})$ 5 2025 156065 11390625 946609025 66556260225 4262469942785 274941996890625 17874140985554945 1150668609575450625

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ -3 9 33 161 897 3969 15873 64001 260097 1046529

## Decomposition

1.4.ae 2 $\times$ 1.4.a

## Base change

This isogeny class is not primitive. It is a base change from the following isogeny classes over subfields of $\F_{2^2}$.

 Subfield Primitive Model $\F_{2}$ 3.2.ac_ac_i $\F_{2}$ 3.2.c_ac_ai