Properties

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

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Invariants

Base field:  $\F_{23}$
Dimension:  $2$
L-polynomial:  $1 - 15 x + 99 x^{2} - 345 x^{3} + 529 x^{4}$
Frobenius angles:  $\pm0.0783210629050$, $\pm0.297557123995$
Angle rank:  $2$ (numerical)
Number field:  4.0.54925.1
Galois group:  $C_4$
Jacobians:  2

This isogeny class is simple and geometrically simple.

Newton polygon

This isogeny class is ordinary.

$p$-rank:  $2$
Slopes:  $[0, 0, 1, 1]$

Point counts

This isogeny class contains the Jacobians of 2 curves, 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 and endomorphism algebra

Endomorphism algebra over $\F_{23}$
The endomorphism algebra of this simple isogeny class is 4.0.54925.1.
All geometric endomorphisms are defined over $\F_{23}$.

Base change

This is a primitive isogeny class.

Twists

Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.23.p_dv$2$(not in LMFDB)