Properties

Label 2.27.an_dn
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:  $1 - 13 x + 91 x^{2} - 351 x^{3} + 729 x^{4}$
Frobenius angles:  $\pm0.179038824787$, $\pm0.3672772547$
Angle rank:  $2$ (numerical)
Number field:  4.0.1222893.2
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
$A(\F_{q^r})$ 457 541545 393354067 282992462925 205899321073552 150097238715453345 109420959439653323191 79766800986219000040725 58149746732038229225022613 42391150550154497915233785600

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 15 743 19983 532499 14349480 387427211 10460541561 282430803731 7625598760821 205891094574518

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.