Properties

Label 2.27.am_dk
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:  $1 - 12 x + 88 x^{2} - 324 x^{3} + 729 x^{4}$
Frobenius angles:  $\pm0.24713929302$, $\pm0.354528994537$
Angle rank:  $2$ (numerical)
Number field:  4.0.295168.1
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
$A(\F_{q^r})$ 482 556228 396725042 283402615824 205889234724962 150081407909684356 109417451356577357426 79766404990268588310528 58149739690327176432582818 42391156907051934589436856388

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 16 762 20152 533270 14348776 387386346 10460206192 282429401630 7625597837392 205891125449562

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.