Properties

Label 2.27.ap_ec
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:  $1 - 15 x + 106 x^{2} - 405 x^{3} + 729 x^{4}$
Frobenius angles:  $\pm0.128139004589$, $\pm0.324695182219$
Angle rank:  $2$ (numerical)
Number field:  4.0.93925.1
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
$A(\F_{q^r})$ 416 522496 390975104 282919044096 205896532346336 150090988526841856 109419617218376757344 79766832907075919155200 58149815196415690433668736 42391166239445669283901808896

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 13 717 19864 532361 14349283 387411078 10460413249 282430916753 7625607739048 205891170776397

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.