Properties

Label 4.3.ah_x_abx_dj
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:  $( 1 - 3 x + 3 x^{2} )( 1 - 4 x + 8 x^{2} - 13 x^{3} + 24 x^{4} - 36 x^{5} + 27 x^{6} )$
Frobenius angles:  $\pm0.102762435325$, $\pm0.166666666667$, $\pm0.278353759721$, $\pm0.64326535244$
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
$A(\F_{q^r})$ 7 5537 409444 59672249 4537455167 281119337072 23392114502071 1922148223120489 150528923543557888 12264624935213421617

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -3 7 21 107 307 727 2237 6803 19740 59567

Decomposition

1.3.ad $\times$ 3.3.ae_i_an

Base change

This is a primitive isogeny class.