Properties

Label 4.3.ah_z_ack_eq
Base Field $\F_{3}$
Dimension $4$
$p$-rank $3$
Does not contain a Jacobian

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Invariants

Base field:  $\F_{3}$
Dimension:  $4$
Weil polynomial:  $( 1 - 3 x + 3 x^{2} )( 1 - 4 x + 10 x^{2} - 20 x^{3} + 30 x^{4} - 36 x^{5} + 27 x^{6} )$
Frobenius angles:  $\pm0.0844416807585$, $\pm0.166666666667$, $\pm0.360432408976$, $\pm0.575465777728$
Angle rank:  $3$ (numerical)

Newton polygon

$p$-rank:  $3$
Slopes:  $[0, 0, 0, 1/2, 1/2, 1, 1, 1]$

Point counts

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

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 8 7168 468608 40628224 3823530328 288872464384 23100875366584 1960516736761856 155090381688685184 12092309005923908608

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -3 11 24 75 267 746 2209 6931 20328 58731

Decomposition

1.3.ad $\times$ 3.3.ae_k_au

Base change

This is a primitive isogeny class.