Properties

Label 2.23.ap_dv
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:  $1 - 15 x + 99 x^{2} - 345 x^{3} + 529 x^{4}$
Frobenius angles:  $\pm0.078321062905$, $\pm0.297557123995$
Angle rank:  $2$ (numerical)
Number field:  4.0.54925.1
Galois group:  $C_4$

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
$A(\F_{q^r})$ 269 266041 148573811 78391907101 41416869240464 21911471163161401 11592512377244065151 6132611311749112475925 3244156376282397194921129 1716156777335196967325783296

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 9 503 12213 280131 6434844 148014587 3404730303 78310996723 1801155696399 41426534049278

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.