# Properties

 Label 2.17.al_ck 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: $( 1 - 7 x + 17 x^{2} )( 1 - 4 x + 17 x^{2} )$ Frobenius angles: $\pm0.177280642489$, $\pm0.338793663197$ Angle rank: $2$ (numerical) Jacobians: 4

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 4 curves, and hence is principally polarizable:

• $y^2=10x^6+16x^5+12x^4+7x^3+3x^2+14x+5$
• $y^2=11x^6+2x^5+6x^4+4x^3+11x^2+8x+16$
• $y^2=15x^6+7x^5+5x^4+12x^3+13x^2+14x+14$
• $y^2=7x^6+13x^5+2x^3+6x^2+5x+14$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 154 84700 24906112 7026712000 2017227550954 582618715571200 168383383307588218 48662203092791904000 14063141011230982642048 4064229053264910897713500

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 7 293 5068 84129 1420727 24137426 410352215 6975902401 118588353436 2015992733093

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{17}$
 The isogeny class factors as 1.17.ah $\times$ 1.17.ae 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 is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.17.ad_g $2$ (not in LMFDB) 2.17.d_g $2$ (not in LMFDB) 2.17.l_ck $2$ (not in LMFDB)