Properties

Label 2.3.ab_c
Base Field $\F_{3}$
Dimension $2$
$p$-rank $2$
Principally polarizable
Contains a Jacobian

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Invariants

Base field:  $\F_{3}$
Dimension:  $2$
Weil polynomial:  $1 - x + 2 x^{2} - 3 x^{3} + 9 x^{4}$
Frobenius angles:  $\pm0.235082516458$, $\pm0.648854628963$
Angle rank:  $2$ (numerical)
Number field:  4.0.3757.1
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
$A(\F_{q^r})$ 8 128 608 8704 72088 505856 4723384 42928128 377524832 3472911488

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 3 13 24 105 293 694 2159 6545 19176 58813

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.