# Properties

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

## 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:

• $y^2=15x^6+16x^5+17x^4+9x^3+12x^2+10x+21$
• $y^2=10x^6+19x^5+9x^4+7x^3+9x+5$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 269 266041 148573811 78391907101 41416869240464 21911471163161401 11592512377244065151 6132611311749112475925 3244156376282397194921129 1716156777335196967325783296

 $r$ 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.
 Twist Extension Degree Common base change 2.23.p_dv $2$ (not in LMFDB)