Properties

 Label 2.17.aj_bz Base Field $\F_{17}$ Dimension $2$ Ordinary No $p$-rank $1$ Principally polarizable Yes Contains a Jacobian Yes

Invariants

 Base field: $\F_{17}$ Dimension: $2$ L-polynomial: $1 - 9 x + 51 x^{2} - 153 x^{3} + 289 x^{4}$ Frobenius angles: $\pm0.223072927732$, $\pm0.393933150683$ Angle rank: $2$ (numerical) Number field: 4.0.290173.1 Galois group: $D_{4}$ Jacobians: 4

This isogeny class is simple and geometrically simple.

Newton polygon

 $p$-rank: $1$ Slopes: $[0, 1/2, 1/2, 1]$

Point counts

This isogeny class contains the Jacobians of 4 curves, and hence is principally polarizable:

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

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 179 90037 25084523 7010010709 2015786994224 582638993341213 168386664616004363 48661319226685136517 14062991191427179169723 4064221499894161540617472

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 9 311 5103 83931 1419714 24138263 410360211 6975775699 118587090069 2015988986366

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{17}$
 The endomorphism algebra of this simple isogeny class is 4.0.290173.1.
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_bz $2$ (not in LMFDB)