Properties

Label 2.9.ae_j
Base Field $\F_{3^2}$
Dimension $2$
$p$-rank $1$
Principally polarizable
Contains a Jacobian

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Invariants

Base field:  $\F_{3^2}$
Dimension:  $2$
Weil polynomial:  $1 - 4 x + 9 x^{2} - 36 x^{3} + 81 x^{4}$
Frobenius angles:  $\pm0.116062854579$, $\pm0.586227887495$
Angle rank:  $2$ (numerical)
Number field:  4.0.2873.1
Galois group:  $D_{4}$

This isogeny class is simple.

Newton polygon

$p$-rank:  $1$
Slopes:  $[0, 1/2, 1/2, 1]$

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
$A(\F_{q^r})$ 51 6681 487152 42444393 3522153891 282836553984 22874357201523 1853888277229257 150119605540311408 12157652072668288281

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 6 84 666 6468 59646 532206 4782462 43066884 387484938 3486780564

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.