Properties

Label 2.23.an_dg
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:  $1 - 13 x + 84 x^{2} - 299 x^{3} + 529 x^{4}$
Frobenius angles:  $\pm0.148876346239$, $\pm0.34686631417$
Angle rank:  $2$ (numerical)
Number field:  4.0.390728.1
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
$A(\F_{q^r})$ 302 279652 150266744 78501672224 41427265132522 21914540102640448 11593141165750547978 6132679909750678416512 3244157725395299694757208 1716155902569999966802061572

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 11 529 12350 280521 6436461 148035322 3404914979 78311872689 1801156445426 41426512933209

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.