# Properties

 Label 2.17.ak_bx Base Field $\F_{17}$ Dimension $2$ Ordinary Yes $p$-rank $2$ Principally polarizable Yes Contains a Jacobian Yes

## Invariants

 Base field: $\F_{17}$ Dimension: $2$ L-polynomial: $1 - 10 x + 49 x^{2} - 170 x^{3} + 289 x^{4}$ Frobenius angles: $\pm0.0454542879392$, $\pm0.428461841097$ Angle rank: $2$ (numerical) Number field: 4.0.142400.3 Galois group: $D_{4}$ 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:

• $y^2=14x^6+15x^5+5x^4+6x^3+10x^2+5x+3$
• $y^2=14x^6+15x^5+5x^4+11x^3+13x^2+10x+7$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 159 82521 23939676 6905439801 2010392171439 582519252414096 168385462895412831 48660970239290954025 14062987964585295365724 4064227007104482349060521

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 8 288 4874 82676 1415908 24133302 410357284 6975725668 118587062858 2015991718128

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{17}$
 The endomorphism algebra of this simple isogeny class is 4.0.142400.3.
All geometric endomorphisms are defined over $\F_{17}$.

## 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 2.17.k_bx $2$ (not in LMFDB)