Properties

Label 2.167.abs_bez
Base field $\F_{167}$
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:  $\F_{167}$
Dimension:  $2$
L-polynomial:  $1 - 44 x + 805 x^{2} - 7348 x^{3} + 27889 x^{4}$
Frobenius angles:  $\pm0.0434254521130$, $\pm0.247924377782$
Angle rank:  $2$ (numerical)
Number field:  4.0.688337.1
Galois group:  $D_{4}$
Jacobians:  $34$

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

$r$ $1$ $2$ $3$ $4$ $5$
$A(\F_{q^r})$ $21303$ $768761361$ $21687450639552$ $604973402008177401$ $16871923575591307449183$

Point counts of the curve

$r$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$
$C(\F_{q^r})$ $124$ $27564$ $4656496$ $777804404$ $129891952124$ $21691955596014$ $3622557435915668$ $604967114690152228$ $101029508510725282000$ $16871927924858890758204$

Jacobians and polarizations

This isogeny class contains the Jacobians of 34 curves (of which all are hyperelliptic), and hence is principally polarizable:

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{167}$.

Endomorphism algebra over $\F_{167}$
The endomorphism algebra of this simple isogeny class is 4.0.688337.1.

Base change

This is a primitive isogeny class.

Twists

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

TwistExtension degreeCommon base change
2.167.bs_bez$2$(not in LMFDB)