Properties

Label 5.3.ac_b_c_m_abg
Base Field $\F_{3}$
Dimension $5$
Ordinary No
$p$-rank $5$

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Invariants

Base field:  $\F_{3}$
Dimension:  $5$
Weil polynomial:  $( 1 - 2 x^{2} + 9 x^{4} )( 1 - 2 x + 3 x^{2} - 2 x^{3} + 9 x^{4} - 18 x^{5} + 27 x^{6} )$
Frobenius angles:  $\pm0.187977698232$, $\pm0.195913276015$, $\pm0.359846707444$, $\pm0.737803084298$, $\pm0.804086723985$
Angle rank:  $4$ (numerical)

Newton polygon

This isogeny class is ordinary.

$p$-rank:  $5$
Slopes:  $[0, 0, 0, 0, 0, 1, 1, 1, 1, 1]$

Point counts

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 144 71424 17641584 7446380544 797373918864 230017182029568 53345113489489392 12023676621501235200 2979447860028439668816 701277720406485880391424

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 2 8 32 144 232 812 2326 6488 19850 57668

Decomposition

2.3.a_ac $\times$ 3.3.ac_d_ac

Base change

This is a primitive isogeny class.