Properties

Label 2.23.am_ct
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:  $1 - 12 x + 71 x^{2} - 276 x^{3} + 529 x^{4}$
Frobenius angles:  $\pm0.0764113711973$, $\pm0.409744704531$
Angle rank:  $1$ (numerical)
Number field:  \(\Q(\sqrt{-3}, \sqrt{11})\)
Galois group:  $V_4$

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
$A(\F_{q^r})$ 313 278257 148032724 78016862889 41382431470873 21913687374860176 11593243563454830121 6132653583584207524425 3244150909896622595595796 1716155716281448713239689777

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 12 528 12168 278788 6429492 148029558 3404945052 78311536516 1801152661464 41426508436368

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.