Properties

Label 2.27.am_dc
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:  $1 - 12 x + 80 x^{2} - 324 x^{3} + 729 x^{4}$
Frobenius angles:  $\pm0.156439426947$, $\pm0.411964257122$
Angle rank:  $2$ (numerical)
Number field:  4.0.3846400.2
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
$A(\F_{q^r})$ 474 543204 390997386 282381340176 205868560616634 150108254542264356 109423032702077662314 79766834031564021448704 58149723443060070385115994 42391151591895087940577642724

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 16 746 19864 531350 14347336 387455642 10460739760 282430920734 7625595706768 205891099634186

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.