Properties

Label 2.23.am_cz
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:  $1 - 12 x + 77 x^{2} - 276 x^{3} + 529 x^{4}$
Frobenius angles:  $\pm0.171291584331$, $\pm0.371639008133$
Angle rank:  $2$ (numerical)
Number field:  4.0.47025.1
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
$A(\F_{q^r})$ 319 285505 150690496 78486752025 41426425940119 21915509540024320 11593283034288701911 6132671453579296178025 3244152545071251754857664 1716155165405637360076572625

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 12 540 12384 280468 6436332 148041870 3404956644 78311764708 1801153569312 41426495138700

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.