Properties

Label 2.167.abv_bhy
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:  $1 - 47 x + 882 x^{2} - 7849 x^{3} + 27889 x^{4}$
Frobenius angles:  $\pm0.0472430896314$, $\pm0.188637795115$
Angle rank:  $2$ (numerical)
Number field:  4.0.219929.1
Galois group:  $D_{4}$
Jacobians:  $12$

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

$r$ $1$ $2$ $3$ $4$ $5$
$A(\F_{q^r})$ $20876$ $765481168$ $21677957802800$ $604962268662857024$ $16871951056366484662996$

Point counts of the curve

$r$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$
$C(\F_{q^r})$ $121$ $27445$ $4654456$ $777790089$ $129892163691$ $21691964264590$ $3622557589898053$ $604967116334678769$ $101029508516127902632$ $16871927924663214553725$

Jacobians and polarizations

This isogeny class contains the Jacobians of 12 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 4.0.219929.1.

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.bv_bhy$2$(not in LMFDB)