Properties

Label 2.23.an_dj
Base Field $\F_{23}$
Dimension $2$
$p$-rank $2$
Principally polarizable
Contains a Jacobian

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Invariants

Base field:  $\F_{23}$
Dimension:  $2$
Weil polynomial:  $1 - 13 x + 87 x^{2} - 299 x^{3} + 529 x^{4}$
Frobenius angles:  $\pm0.207871921947$, $\pm0.310374946937$
Angle rank:  $2$ (numerical)
Number field:  4.0.53525.1
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
$A(\F_{q^r})$ 305 283345 151716455 78782660525 41453629822000 21913923394751905 11592551853137515355 6132586603119719513525 3244150319110100899204805 1716155819482392132014368000

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 11 535 12467 281523 6440556 148031155 3404741897 78310681203 1801152333461 41426510927550

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.