Properties

Label 2.16.ah_y
Base Field $\F_{2^{4}}$
Dimension $2$
Ordinary No
$p$-rank $1$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{2^{4}}$
Dimension:  $2$
L-polynomial:  $( 1 - 4 x )^{2}( 1 + x + 16 x^{2} )$
Frobenius angles:  $0$, $0$, $\pm0.539893087675$
Angle rank:  $1$ (numerical)
Jacobians:  1

This isogeny class is not simple.

Newton polygon

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

Point counts

This isogeny class contains the Jacobians of 1 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 162 64800 16074450 4232347200 1098623120562 281437900380000 72042035002383762 18445878221841820800 4722363007271186152050 1208924233678783668420000

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 10 256 3922 64576 1047730 16775008 268377490 4294765696 68719426162 1099510185376

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{4}}$
The isogeny class factors as 1.16.ai $\times$ 1.16.b 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 are some of the twists of this isogeny class.
TwistExtension DegreeCommon base change
2.16.aj_bo$2$2.256.ab_asm
2.16.h_y$2$2.256.ab_asm
2.16.j_bo$2$2.256.ab_asm
2.16.f_bk$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.16.aj_bo$2$2.256.ab_asm
2.16.h_y$2$2.256.ab_asm
2.16.j_bo$2$2.256.ab_asm
2.16.f_bk$3$(not in LMFDB)
2.16.ab_bg$4$(not in LMFDB)
2.16.b_bg$4$(not in LMFDB)
2.16.af_bk$6$(not in LMFDB)
2.16.ad_bc$6$(not in LMFDB)
2.16.d_bc$6$(not in LMFDB)