# Properties

 Label 2.17.ao_df 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: $( 1 - 7 x + 17 x^{2} )^{2}$ Frobenius angles: $\pm0.177280642489$, $\pm0.177280642489$ Angle rank: $1$ (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:

• $y^2=6x^6+16x^4+4x^3+2x^2+3$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 121 75625 24285184 7035015625 2022342812281 583087267840000 168401996374543129 48661783896050015625 14063036162888693026816 4064222751691998577515625

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 4 260 4942 84228 1424324 24156830 410397572 6975842308 118587469294 2015989607300

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{17}$
 The isogeny class factors as 1.17.ah 2 and its endomorphism algebra is $\mathrm{M}_{2}($$$\Q(\sqrt{-19})$$$)$
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.a_ap $2$ (not in LMFDB) 2.17.o_df $2$ (not in LMFDB) 2.17.h_bg $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.17.a_ap $2$ (not in LMFDB) 2.17.o_df $2$ (not in LMFDB) 2.17.h_bg $3$ (not in LMFDB) 2.17.a_p $4$ (not in LMFDB) 2.17.ah_bg $6$ (not in LMFDB)