# Properties

 Label 2.17.aj_bq 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: $( 1 - 8 x + 17 x^{2} )( 1 - x + 17 x^{2} )$ Frobenius angles: $\pm0.0779791303774$, $\pm0.461304015105$ Angle rank: $2$ (numerical) Jacobians: 2

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 2 curves, and hence is principally polarizable:

• $y^2=2x^5+5x^3+16x^2+12x+6$
• $y^2=7x^6+5x^5+16x^4+12x^3+10x^2+16x+10$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 170 83980 23876840 6906515200 2012918167850 582775213895680 168392714234005130 48660977581413350400 14063060265109115260520 4064237805908290336693900

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 9 293 4860 82689 1417689 24143906 410374953 6975726721 118587672540 2015997074693

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{17}$
 The isogeny class factors as 1.17.ai $\times$ 1.17.ab 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.ah_ba $2$ (not in LMFDB) 2.17.h_ba $2$ (not in LMFDB) 2.17.j_bq $2$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.17.ah_ba $2$ (not in LMFDB) 2.17.h_ba $2$ (not in LMFDB) 2.17.j_bq $2$ (not in LMFDB) 2.17.ad_bk $4$ (not in LMFDB) 2.17.ab_bg $4$ (not in LMFDB) 2.17.b_bg $4$ (not in LMFDB) 2.17.d_bk $4$ (not in LMFDB)