Properties

Label 2.27.an_df
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:  $1 - 13 x + 83 x^{2} - 351 x^{3} + 729 x^{4}$
Frobenius angles:  $\pm0.0702760081003$, $\pm0.411256475822$
Angle rank:  $2$ (numerical)
Number field:  4.0.1452253.1
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
$A(\F_{q^r})$ 449 528473 387157883 281598423469 205735242292624 150089367579034961 109420921356511391887 79766685321056825335893 58149729135574209729478589 42391156246532123707740217088

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 15 727 19671 529875 14338040 387406891 10460537921 282430394195 7625596453269 205891122241462

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.