Properties

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

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Invariants

Base field:  $\F_{2^{4}}$
Dimension:  $2$
L-polynomial:  $( 1 - 5 x + 16 x^{2} )^{2}$
Frobenius angles:  $\pm0.285098958592$, $\pm0.285098958592$
Angle rank:  $1$ (numerical)
Jacobians:  6

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 6 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 144 69696 17740944 4356000000 1100510098704 281306156129856 72040005072846864 18446028573456000000 4722381292753126898064 1208929935151727208484416

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 7 271 4327 66463 1049527 16767151 268369927 4294800703 68719692247 1099515370831

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{4}}$
The isogeny class factors as 1.16.af 2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-39}) \)$)$
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.
TwistExtension DegreeCommon base change
2.16.a_h$2$2.256.o_vp
2.16.k_cf$2$2.256.o_vp
2.16.f_j$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.16.a_h$2$2.256.o_vp
2.16.k_cf$2$2.256.o_vp
2.16.f_j$3$(not in LMFDB)
2.16.a_ah$4$(not in LMFDB)
2.16.af_j$6$(not in LMFDB)