Properties

Label 2.181.abx_bkx
Base field $\F_{181}$
Dimension $2$
$p$-rank $2$
Ordinary yes
Supersingular no
Simple yes
Geometrically simple yes
Primitive yes
Principally polarizable yes
Contains a Jacobian yes

Related objects

Downloads

Learn more

Invariants

Base field:  $\F_{181}$
Dimension:  $2$
L-polynomial:  $1 - 49 x + 959 x^{2} - 8869 x^{3} + 32761 x^{4}$
Frobenius angles:  $\pm0.0675982025699$, $\pm0.180470077574$
Angle rank:  $2$ (numerical)
Number field:  4.0.1135173.1
Galois group:  $D_{4}$
Jacobians:  $10$

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

$r$ $1$ $2$ $3$ $4$ $5$
$A(\F_{q^r})$ $24803$ $1057575117$ $35142370370207$ $1151935362697290453$ $37738676653843304208848$

Point counts of the curve

$r$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$
$C(\F_{q^r})$ $133$ $32279$ $5926459$ $1073281915$ $194264655718$ $35161836321215$ $6364291021791115$ $1151936658475079923$ $208500535064710937965$ $37738596846842066811974$

Jacobians and polarizations

This isogeny class contains the Jacobians of 10 curves (of which all are hyperelliptic), and hence is principally polarizable:

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{181}$.

Endomorphism algebra over $\F_{181}$
The endomorphism algebra of this simple isogeny class is 4.0.1135173.1.

Base change

This is a primitive isogeny class.

Twists

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

TwistExtension degreeCommon base change
2.181.bx_bkx$2$(not in LMFDB)