Properties

Label 2.27.am_ct
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:  $1 - 12 x + 71 x^{2} - 324 x^{3} + 729 x^{4}$
Frobenius angles:  $\pm0.0255291991662$, $\pm0.449522792481$
Angle rank:  $2$ (numerical)
Number field:  4.0.421648.1
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
$A(\F_{q^r})$ 465 528705 384590340 281072795625 205713673746825 150089969182052880 109419094435543704465 79766113254799420175625 58149663709129202887968420 42391154078644330001577503025

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 16 728 19540 528884 14336536 387408446 10460363272 282428368676 7625587873420 205891111712168

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.