# Properties

 Label 2.17.al_cg 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: $( 1 - 8 x + 17 x^{2} )( 1 - 3 x + 17 x^{2} )$ Frobenius angles: $\pm0.0779791303774$, $\pm0.381477984739$ Angle rank: $2$ (numerical) Jacobians: 3

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 3 curves, and hence is principally polarizable:

• $y^2=3x^6+16x^5+4x^4+2x^3+6x^2+5$
• $y^2=11x^6+11x^5+9x^4+3x^3+3x^2+4x+7$
• $y^2=7x^6+11x^5+3x^4+6x^3+15x^2+3$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 150 81900 24242400 6945120000 2011609803750 582452363001600 168388692037314150 48662783705128320000 14063149824404621522400 4064231032629148100947500

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 7 285 4936 83153 1416767 24130530 410365151 6975985633 118588427752 2015993714925

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{17}$
 The isogeny class factors as 1.17.ai $\times$ 1.17.ad 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.af_k $2$ (not in LMFDB) 2.17.f_k $2$ (not in LMFDB) 2.17.l_cg $2$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.17.af_k $2$ (not in LMFDB) 2.17.f_k $2$ (not in LMFDB) 2.17.l_cg $2$ (not in LMFDB) 2.17.af_bo $4$ (not in LMFDB) 2.17.ab_bc $4$ (not in LMFDB) 2.17.b_bc $4$ (not in LMFDB) 2.17.f_bo $4$ (not in LMFDB)