# Properties

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

# Learn more about

## Invariants

 Base field: $\F_{17}$ Dimension: $2$ L-polynomial: $1 - 9 x + 46 x^{2} - 153 x^{3} + 289 x^{4}$ Frobenius angles: $\pm0.147872872551$, $\pm0.436753511906$ Angle rank: $2$ (numerical) Number field: 4.0.971388.2 Galois group: $D_{4}$ Jacobians: 10

This isogeny class is simple and geometrically 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 10 curves, and hence is principally polarizable:

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

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 174 86652 24410808 6955729344 2015469561774 582932438477568 168410708192052318 48662191704444602112 14063046087231918221688 4064229474706288087398972

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 9 301 4968 83281 1419489 24150418 410418801 6975900769 118587552984 2015992942141

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{17}$
 The endomorphism algebra of this simple isogeny class is 4.0.971388.2.
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.j_bu $2$ (not in LMFDB)