# Properties

 Label 2.17.ak_cb 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: $1 - 10 x + 53 x^{2} - 170 x^{3} + 289 x^{4}$ Frobenius angles: $\pm0.141075462221$, $\pm0.399907016694$ Angle rank: $2$ (numerical) Number field: 4.0.442944.2 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:

• $y^2=12x^6+10x^5+15x^4+7x^3+5x^2+2x+10$
• $y^2=10x^6+8x^5+x^4+11x^3+4x^2+13x+10$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 163 85249 24536716 6970725481 2014644459643 582758684476816 168407869599292507 48663207639232067529 14063113492007835514444 4064227265971277058006049

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 8 296 4994 83460 1418908 24143222 410411884 6976046404 118588121378 2015991846536

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{17}$
 The endomorphism algebra of this simple isogeny class is 4.0.442944.2.
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_cb $2$ (not in LMFDB)