Properties

Label 2.27.aq_el
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:  $1 - 16 x + 115 x^{2} - 432 x^{3} + 729 x^{4}$
Frobenius angles:  $\pm0.114075220034$, $\pm0.29391853863$
Angle rank:  $2$ (numerical)
Number field:  4.0.131472.2
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
$A(\F_{q^r})$ 397 513321 389944516 282984114201 205925369789677 150091754588120592 109418609366581738501 79766596872822180725673 58149797530547187983834212 42391169416656473490774654441

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 12 704 19812 532484 14351292 387413054 10460316900 282430081028 7625605422396 205891186207904

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.