Properties

Label 2.211.acb_brd
Base field $\F_{211}$
Dimension $2$
$p$-rank $2$
Ordinary yes
Supersingular no
Simple yes
Geometrically simple yes
Primitive yes
Principally polarizable yes
Contains a Jacobian yes

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Invariants

Base field:  $\F_{211}$
Dimension:  $2$
L-polynomial:  $1 - 53 x + 1121 x^{2} - 11183 x^{3} + 44521 x^{4}$
Frobenius angles:  $\pm0.0724318417965$, $\pm0.176533229289$
Angle rank:  $2$ (numerical)
Number field:  4.0.188773.1
Galois group:  $D_{4}$
Jacobians:  $15$

This isogeny class is simple and geometrically simple, primitive, ordinary, and not supersingular. It is principally polarizable and contains a Jacobian.

Newton polygon

This isogeny class is ordinary.

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

Point counts

Point counts of the abelian variety

$r$ $1$ $2$ $3$ $4$ $5$
$A(\F_{q^r})$ $34407$ $1957035753$ $88206623320113$ $3928795657851881853$ $174914270143095943440432$

Point counts of the curve

$r$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$
$C(\F_{q^r})$ $159$ $43955$ $9389745$ $1982118523$ $418227865824$ $88245954263063$ $18619893469962363$ $3928797480448301059$ $828976267950911695233$ $174913992535330594085990$

Jacobians and polarizations

This isogeny class contains the Jacobians of 15 curves (of which all are hyperelliptic), and hence is principally polarizable:

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{211}$.

Endomorphism algebra over $\F_{211}$
The endomorphism algebra of this simple isogeny class is 4.0.188773.1.

Base change

This is a primitive isogeny class.

Twists

Below is a list of all twists of this isogeny class.

TwistExtension degreeCommon base change
2.211.cb_brd$2$(not in LMFDB)