Properties

Label 2.27.ap_ea
Base Field $\F_{3^3}$
Dimension $2$
$p$-rank $2$
Principally polarizable
Contains a Jacobian

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Invariants

Base field:  $\F_{3^3}$
Dimension:  $2$
Weil polynomial:  $( 1 - 10 x + 27 x^{2} )( 1 - 5 x + 27 x^{2} )$
Frobenius angles:  $\pm0.0877398280459$, $\pm0.340228233311$
Angle rank:  $2$ (numerical)

Newton polygon

This isogeny class is ordinary.

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

Point counts

This isogeny class contains a Jacobian, and hence is principally polarizable.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 414 519156 389178216 282408404256 205806150001314 150080778688268736 109418962630098979026 79766813656768637520000 58149811570670246994633864 42391165536482964757613303796

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 13 713 19774 531401 14342983 387384722 10460350669 282430848593 7625607263578 205891167362153

Decomposition

1.27.ak $\times$ 1.27.af

Base change

This is a primitive isogeny class.