Properties

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

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Invariants

Base field:  $\F_{2^2}$
Dimension:  $3$
Weil polynomial:  $( 1 - 2 x + 4 x^{2} )( 1 - 5 x + 13 x^{2} - 20 x^{3} + 16 x^{4} )$
Frobenius angles:  $\pm0.140237960897$, $\pm0.333333333333$, $\pm0.38771221219$
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.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 15 5775 390420 18093075 1015466625 67339641600 4475694267465 286746307923075 18135341747548020 1152641822571421875

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -2 22 91 274 968 4015 16672 66754 263899 1048322

Decomposition

1.4.ac $\times$ 2.4.af_n

Base change

This is a primitive isogeny class.