# Properties

 Label 2.17.ap_dm Base Field $\F_{17}$ Dimension $2$ Ordinary Yes $p$-rank $2$ Principally polarizable Yes Contains a Jacobian No

## Invariants

 Base field: $\F_{17}$ Dimension: $2$ L-polynomial: $( 1 - 8 x + 17 x^{2} )( 1 - 7 x + 17 x^{2} )$ Frobenius angles: $\pm0.0779791303774$, $\pm0.177280642489$ Angle rank: $2$ (numerical) Jacobians: 0

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 is principally polarizable, but does not contain a Jacobian.

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 110 71500 23703680 6978400000 2018018233550 582830824576000 168392298144692270 48661929864662400000 14063108690397910183040 4064231487841064613287500

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 3 245 4824 83553 1421283 24146210 410373939 6975863233 118588080888 2015993940725

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{17}$
 The isogeny class factors as 1.17.ai $\times$ 1.17.ah 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.ab_aw $2$ (not in LMFDB) 2.17.b_aw $2$ (not in LMFDB) 2.17.p_dm $2$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.17.ab_aw $2$ (not in LMFDB) 2.17.b_aw $2$ (not in LMFDB) 2.17.p_dm $2$ (not in LMFDB) 2.17.aj_bw $4$ (not in LMFDB) 2.17.af_u $4$ (not in LMFDB) 2.17.f_u $4$ (not in LMFDB) 2.17.j_bw $4$ (not in LMFDB)