# Properties

 Label 2.17.ak_cd Base Field $\F_{17}$ Dimension $2$ Ordinary Yes $p$-rank $2$ Principally polarizable Yes Contains a Jacobian Yes

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## Invariants

 Base field: $\F_{17}$ Dimension: $2$ L-polynomial: $( 1 - 7 x + 17 x^{2} )( 1 - 3 x + 17 x^{2} )$ Frobenius angles: $\pm0.177280642489$, $\pm0.381477984739$ Angle rank: $2$ (numerical) Jacobians: 18

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 18 curves, and hence is principally polarizable:

• $y^2=11x^6+14x^5+10x^4+6x^3+5x+14$
• $y^2=10x^6+x^5+5x^4+2x^3+14x^2+16x+6$
• $y^2=5x^6+12x^5+4x^4+13x^3+4x^2+12x+5$
• $y^2=11x^6+6x^5+6x^4+11x^3+12x^2+7x+3$
• $y^2=16x^6+3x^5+6x^4+6x^3+5x^2+12x+8$
• $y^2=11x^6+6x^5+5x^4+6x^3+8x^2+12x+6$
• $y^2=14x^6+10x^5+4x^4+13x^2+10x+3$
• $y^2=13x^6+4x^5+5x^4+4x^3+6x^2+3x+14$
• $y^2=3x^6+4x^5+13x^4+4x^3+13x^2+3x+14$
• $y^2=5x^6+6x^5+2x^4+11x^3+8x^2+11x+14$
• $y^2=10x^6+16x^5+6x^4+15x^3+7x^2+1$
• $y^2=10x^6+2x^5+12x^4+8x^3+5x^2+2x+7$
• $y^2=14x^6+2x^5+10x^4+5x^3+10x^2+14$
• $y^2=10x^6+7x^5+9x^4+4x^3+9x^2+7x+10$
• $y^2=6x^6+16x^5+x^4+6x^3+9x^2+4x+7$
• $y^2=7x^6+2x^5+11x^4+4x^3+7x^2+15x+11$
• $y^2=10x^6+6x^5+6x^4+11x^3+4x^2+11x+12$
• $y^2=6x^6+8x^5+7x^4+13x^3+14x^2+3x+12$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 165 86625 24837120 7001465625 2015920649325 582708639744000 168398390059478205 48662637733954715625 14063077296683264424960 4064222296481060552540625

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 8 300 5054 83828 1419808 24141150 410388784 6975964708 118587816158 2015989381500

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{17}$
 The isogeny class factors as 1.17.ah $\times$ 1.17.ad 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.ae_n $2$ (not in LMFDB) 2.17.e_n $2$ (not in LMFDB) 2.17.k_cd $2$ (not in LMFDB)