# Properties

 Label 2.17.an_cw 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: $( 1 - 8 x + 17 x^{2} )( 1 - 5 x + 17 x^{2} )$ Frobenius angles: $\pm0.0779791303774$, $\pm0.292637436158$ Angle rank: $2$ (numerical) Jacobians: 1

This isogeny class is not 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:

• $y^2=5x^6+5x^5+3x^2+9x+6$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 130 77740 24261640 6990380800 2015239733650 582427647143680 168363781664704210 48661076024196480000 14063166150216570691720 4064241387720474658254700

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 5 269 4940 83697 1419325 24129506 410304445 6975740833 118588565420 2015998851389

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{17}$
 The isogeny class factors as 1.17.ai $\times$ 1.17.af and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:
All geometric endomorphisms are defined over $\F_{17}$.

## Base change

This is a primitive isogeny class.

## Twists

Below are some of the twists of this isogeny class.
 Twist Extension Degree Common base change 2.17.ad_ag $2$ (not in LMFDB) 2.17.d_ag $2$ (not in LMFDB) 2.17.n_cw $2$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.17.ad_ag $2$ (not in LMFDB) 2.17.d_ag $2$ (not in LMFDB) 2.17.n_cw $2$ (not in LMFDB) 2.17.ah_bs $4$ (not in LMFDB) 2.17.ad_y $4$ (not in LMFDB) 2.17.d_y $4$ (not in LMFDB) 2.17.h_bs $4$ (not in LMFDB)