Properties

Label 2.27.an_do
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:  $1 - 13 x + 92 x^{2} - 351 x^{3} + 729 x^{4}$
Frobenius angles:  $\pm0.191829796935$, $\pm0.359538824879$
Angle rank:  $2$ (numerical)
Number field:  4.0.885496.1
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
$A(\F_{q^r})$ 458 543188 394130984 283157386144 205911447386518 150094774329406400 109420116057788602342 79766688284624403391104 58149740577966470400925256 42391150815899522064700041428

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 15 745 20022 532809 14350325 387420850 10460460935 282430404689 7625597953794 205891095865225

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.