Properties

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

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Invariants

Base field:  $\F_{3^2}$
Dimension:  $2$
Weil polynomial:  $1 - 4 x + 8 x^{2} - 36 x^{3} + 81 x^{4}$
Frobenius angles:  $\pm0.0937471905441$, $\pm0.593747190544$
Angle rank:  $1$ (numerical)
Number field:  \(\Q(i, \sqrt{14})\)
Galois group:  $C_2^2$

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
$A(\F_{q^r})$ 50 6500 478850 42250000 3512625250 282430518500 22868203853650 1853819136000000 150115276930190450 12157665452614662500

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 6 82 654 6438 59486 531442 4781174 43065278 387473766 3486784402

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.