# Properties

 Label 2.16.ao_dd 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: $( 1 - 7 x + 16 x^{2} )^{2}$ Frobenius angles: $\pm0.160861246510$, $\pm0.160861246510$ Angle rank: $1$ (numerical) Jacobians: 1

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 1 curves, and hence is principally polarizable:

• $y^2+(x^2+x)y=x^5+a^3x^4+x^3+(a^3+1)x^2+x$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 100 57600 16728100 4324377600 1103025062500 281748310329600 72073826707176100 18447442819965849600 4722378257821885008100 1208924276393377476000000

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 3 223 4083 65983 1051923 16793503 268495923 4295129983 68719648083 1099510224223

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{4}}$
 The isogeny class factors as 1.16.ah 2 and its endomorphism algebra is $\mathrm{M}_{2}($$$\Q(\sqrt{-15})$$$)$
All geometric endomorphisms are defined over $\F_{2^{4}}$.

## Base change

This is a primitive isogeny class.

## Twists

Below are some of the twists of this isogeny class.
 Twist Extension Degree Common base change 2.16.a_ar $2$ 2.256.abi_bev 2.16.o_dd $2$ 2.256.abi_bev 2.16.h_bh $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.16.a_ar $2$ 2.256.abi_bev 2.16.o_dd $2$ 2.256.abi_bev 2.16.h_bh $3$ (not in LMFDB) 2.16.a_r $4$ (not in LMFDB) 2.16.ah_bh $6$ (not in LMFDB)