Properties

Label 2.16.an_cu
Base field $\F_{2^{4}}$
Dimension $2$
$p$-rank $1$
Ordinary no
Supersingular no
Simple no
Geometrically simple no
Primitive yes
Principally polarizable yes
Contains a Jacobian no

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Invariants

Base field:  $\F_{2^{4}}$
Dimension:  $2$
L-polynomial:  $( 1 - 4 x )^{2}( 1 - 5 x + 16 x^{2} )$
  $1 - 13 x + 72 x^{2} - 208 x^{3} + 256 x^{4}$
Frobenius angles:  $0$, $0$, $\pm0.285098958592$
Angle rank:  $1$ (numerical)
Jacobians:  $0$

This isogeny class is not simple, primitive, not ordinary, and not supersingular. It is principally polarizable.

Newton polygon

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

Point counts

Point counts of the abelian variety

$r$ $1$ $2$ $3$ $4$ $5$
$A(\F_{q^r})$ $108$ $59400$ $16717428$ $4291650000$ $1097863340508$

Point counts of the (virtual) curve

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

Jacobians and polarizations

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

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{2^{4}}$.

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:

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)