# Properties

 Label 2.16.am_cp Base Field $\F_{2^{4}}$ Dimension $2$ Ordinary Yes $p$-rank $2$ Principally polarizable Yes Contains a Jacobian Yes

## Invariants

 Base field: $\F_{2^{4}}$ Dimension: $2$ L-polynomial: $( 1 - 7 x + 16 x^{2} )( 1 - 5 x + 16 x^{2} )$ Frobenius angles: $\pm0.160861246510$, $\pm0.285098958592$ Angle rank: $2$ (numerical) Jacobians: 8

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 8 curves, and hence is principally polarizable:

• $y^2+(x^2+x+a^3+a^2+1)y=a^2x^5+a^2x^3+(a^3+a+1)x^2+(a^2+a)x+a^2+a$
• $y^2+(x^2+x+a^3)y=(a+1)x^5+(a+1)x^3+(a^3+1)x^2+(a^3+a^2+a)x+a^2$
• $y^2+(x^2+x+a^3+a^2+a)y=(a^2+1)x^5+(a^2+1)x^3+(a^3+a^2+1)x^2+(a^3+a^2)x+a^3+a$
• $y^2+(x^2+x+a^3)y=(a^2+a+1)x^5+(a^2+a+1)x^3+(a^3+a^2)x^2+(a^3+a^2+a)x+a^3+a$
• $y^2+(x^2+x+a^3+1)y=ax^5+ax^3+(a^3+a^2+a)x^2+(a^2+a+1)x+a^2+a+1$
• $y^2+(x^2+x+a^3+a)y=(a^2+a)x^5+(a^2+a)x^3+a^3x^2+(a^3+a^2+1)x+a^3+a^2+a+1$
• $y^2+(x^2+x+a^3+a^2+a+1)y=(a^2+a+1)x^5+(a^2+a+1)x^3+(a^3+a)x^2+(a^3+1)x+a^3+a^2$
• $y^2+(x^2+x+a^3+a^2)y=(a^2+a)x^5+(a^2+a)x^3+(a^3+a^2+a+1)x^2+(a^3+a+1)x+a^3$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 120 63360 17227080 4340160000 1101766863000 281527146426240 72056913905637480 18446735683157760000 4722379775287262145720 1208927105769241395504000

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 5 247 4205 66223 1050725 16780327 268432925 4294965343 68719670165 1099512797527

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{4}}$
 The isogeny class factors as 1.16.ah $\times$ 1.16.af 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 $\F_{2^{4}}$.

## 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 2.16.ac_ad $2$ 2.256.ak_pd 2.16.c_ad $2$ 2.256.ak_pd 2.16.m_cp $2$ 2.256.ak_pd