# Properties

 Label 2.17.ao_de 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: $( 1 - 8 x + 17 x^{2} )( 1 - 6 x + 17 x^{2} )$ Frobenius angles: $\pm0.0779791303774$, $\pm0.240632536990$ 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:

• $y^2=10x^6+8x^5+8x^4+2x^3+8x^2+8x+10$
• $y^2=12x^6+x^5+8x^3+13x+7$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 120 74880 24069240 6996787200 2017565556600 582640049047680 168371111648329080 48660500749182566400 14063061977523943296120 4064234154788176529846400

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 4 258 4900 83774 1420964 24138306 410322308 6975658366 118587686980 2015995263618

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{17}$
 The isogeny class factors as 1.17.ai $\times$ 1.17.ag 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.ac_ao $2$ (not in LMFDB) 2.17.c_ao $2$ (not in LMFDB) 2.17.o_de $2$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.17.ac_ao $2$ (not in LMFDB) 2.17.c_ao $2$ (not in LMFDB) 2.17.o_de $2$ (not in LMFDB) 2.17.ai_bu $4$ (not in LMFDB) 2.17.ae_w $4$ (not in LMFDB) 2.17.e_w $4$ (not in LMFDB) 2.17.i_bu $4$ (not in LMFDB)