Properties

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

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Invariants

Base field:  $\F_{2^{4}}$
Dimension:  $2$
L-polynomial:  $( 1 - 4 x )^{2}( 1 - 5 x + 16 x^{2} )$
Frobenius angles:  $0$, $0$, $\pm0.285098958592$
Angle rank:  $1$ (numerical)
Jacobians:  0

This isogeny class is not simple.

Newton polygon

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

Point counts

This isogeny class is principally polarizable, but does not contain a Jacobian.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 108 59400 16717428 4291650000 1097863340508 281253172800600 72040004267638788 18445823385372900000 4722337859020785820908 1208925571535592304185000

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 4 232 4084 65488 1047004 16763992 268369924 4294752928 68719060204 1099511402152

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{4}}$
The isogeny class factors as 1.16.ai $\times$ 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 are some of the twists of this isogeny class.
TwistExtension DegreeCommon base change
2.16.ad_ai$2$2.256.az_lc
2.16.d_ai$2$2.256.az_lc
2.16.n_cu$2$2.256.az_lc
2.16.ab_m$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.16.ad_ai$2$2.256.az_lc
2.16.d_ai$2$2.256.az_lc
2.16.n_cu$2$2.256.az_lc
2.16.ab_m$3$(not in LMFDB)
2.16.af_bg$4$(not in LMFDB)
2.16.f_bg$4$(not in LMFDB)
2.16.aj_ca$6$(not in LMFDB)
2.16.b_m$6$(not in LMFDB)
2.16.j_ca$6$(not in LMFDB)