Properties

 Label 2.17.aj_ca 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: $( 1 - 6 x + 17 x^{2} )( 1 - 3 x + 17 x^{2} )$ Frobenius angles: $\pm0.240632536990$, $\pm0.381477984739$ Angle rank: $2$ (numerical) Jacobians: 9

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 9 curves, and hence is principally polarizable:

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

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 180 90720 25220160 7019913600 2015468442900 582517904209920 168377202796652820 48661208597686003200 14063030583913576802880 4064224963422141102261600

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 9 313 5130 84049 1419489 24133246 410337153 6975759841 118587422250 2015990704393

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{17}$
 The isogeny class factors as 1.17.ag $\times$ 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.ad_q $2$ (not in LMFDB) 2.17.d_q $2$ (not in LMFDB) 2.17.j_ca $2$ (not in LMFDB)