Properties

Label 2.157.abq_bco
Base field $\F_{157}$
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:  $\F_{157}$
Dimension:  $2$
L-polynomial:  $1 - 42 x + 742 x^{2} - 6594 x^{3} + 24649 x^{4}$
Frobenius angles:  $\pm0.0607074138189$, $\pm0.255796322361$
Angle rank:  $2$ (numerical)
Number field:  4.0.137904.1
Galois group:  $D_{4}$
Jacobians:  $60$

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

$r$ $1$ $2$ $3$ $4$ $5$
$A(\F_{q^r})$ $18756$ $600717168$ $14974607060100$ $369153415717012224$ $9099063502786454981796$

Point counts of the curve

$r$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$
$C(\F_{q^r})$ $116$ $24370$ $3869516$ $607586734$ $95389030316$ $14976067785730$ $2351243178148148$ $369145193316384094$ $57955795541366288132$ $9099059901136920888850$

Jacobians and polarizations

This isogeny class contains the Jacobians of 60 curves (of which all are hyperelliptic), and hence is principally polarizable:

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{157}$.

Endomorphism algebra over $\F_{157}$
The endomorphism algebra of this simple isogeny class is 4.0.137904.1.

Base change

This is a primitive isogeny class.

Twists

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

TwistExtension degreeCommon base change
2.157.bq_bco$2$(not in LMFDB)