Properties

 Label 2.17.aj_bx 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: $1 - 9 x + 49 x^{2} - 153 x^{3} + 289 x^{4}$ Frobenius angles: $\pm0.191982029838$, $\pm0.413688260814$ Angle rank: $2$ (numerical) Number field: 4.0.609021.1 Galois group: $D_{4}$ Jacobians: 8

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 8 curves, and hence is principally polarizable:

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

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 177 88677 24814161 6989255109 2016042350352 582819653602341 168401400838004049 48661717364683726725 14062978166342579447409 4064220658854933316042752

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 9 307 5049 83683 1419894 24145747 410396121 6975832771 118586980233 2015988569182

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{17}$
 The endomorphism algebra of this simple isogeny class is 4.0.609021.1.
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_bx $2$ (not in LMFDB)