Properties

Label 2.27.ap_ed
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:  $1 - 15 x + 107 x^{2} - 405 x^{3} + 729 x^{4}$
Frobenius angles:  $\pm0.147061171708$, $\pm0.315307297882$
Angle rank:  $2$ (numerical)
Number field:  4.0.273949.1
Galois group:  $D_{4}$

This isogeny class is simple.

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
$A(\F_{q^r})$ 417 524169 391874499 283171294701 205938502980432 150094477029258801 109419417313844236743 79766719456553600765589 58149795934258609776369021 42391164058444101712824417024

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 13 719 19909 532835 14352208 387420083 10460394139 282430515059 7625605213063 205891160183414

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.