# Properties

 Label 2.17.al_cf 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: $1 - 11 x + 57 x^{2} - 187 x^{3} + 289 x^{4}$ Frobenius angles: $\pm0.0363222529514$, $\pm0.389420801446$ Angle rank: $2$ (numerical) Number field: 4.0.44573.1 Galois group: $D_{4}$ Jacobians: 1

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 1 curves, and hence is principally polarizable:

• $y^2=3x^6+2x^5+3x^4+6x^3+8x^2+7x+10$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 149 81205 24077357 6923944325 2009816552704 582322075016005 168377063814286973 48661568906378867525 14063040965304164776373 4064223610137057085542400

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 7 283 4903 82899 1415502 24125131 410336815 6975811491 118587509791 2015990033118

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{17}$
 The endomorphism algebra of this simple isogeny class is 4.0.44573.1.
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.l_cf $2$ (not in LMFDB)