Properties

Label 3.9.am_cv_akl
Base Field $\F_{3^2}$
Dimension $3$
$p$-rank $3$
Does not contain a Jacobian

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Invariants

Base field:  $\F_{3^2}$
Dimension:  $3$
Weil polynomial:  $( 1 - 5 x + 9 x^{2} )( 1 - 7 x + 29 x^{2} - 63 x^{3} + 81 x^{4} )$
Frobenius angles:  $\pm0.186429498677$, $\pm0.220419591014$, $\pm0.370053256546$
Angle rank:  $3$ (numerical)

Newton polygon

This isogeny class is ordinary.

$p$-rank:  $3$
Slopes:  $[0, 0, 0, 1, 1, 1]$

Point counts

This isogeny class does not contain a Jacobian, and it is unknown whether it is principally polarizable.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 205 556575 436926340 294486615375 207644396614400 150379175500660800 109491169655512844285 79773325389996793023375 58143703951078797628055620 42387854878870482915310080000

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -2 84 817 6836 59553 532449 4786122 43050436 387380293 3486512679

Decomposition

1.9.af $\times$ 2.9.ah_bd

Base change

This is a primitive isogeny class.