Properties

Label 2.173.aby_blj
Base field $\F_{173}$
Dimension $2$
$p$-rank $2$
Ordinary yes
Supersingular no
Simple no
Geometrically simple no
Primitive yes
Principally polarizable yes
Contains a Jacobian yes

Related objects

Downloads

Learn more

Invariants

Base field:  $\F_{173}$
Dimension:  $2$
L-polynomial:  $( 1 - 25 x + 173 x^{2} )^{2}$
  $1 - 50 x + 971 x^{2} - 8650 x^{3} + 29929 x^{4}$
Frobenius angles:  $\pm0.100717649571$, $\pm0.100717649571$
Angle rank:  $1$ (numerical)
Jacobians:  $3$

This isogeny class is not 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

$r$ $1$ $2$ $3$ $4$ $5$
$A(\F_{q^r})$ $22201$ $879181801$ $26781328804624$ $802326964224789481$ $24013810603530039138961$

Point counts of the curve

$r$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$
$C(\F_{q^r})$ $124$ $29372$ $5172418$ $895709076$ $154963909844$ $26808759997958$ $4637914490027348$ $802359181412295268$ $138808137921470311114$ $24013807853230645957772$

Jacobians and polarizations

This isogeny class contains the Jacobians of 3 curves (of which all are hyperelliptic), and hence is principally polarizable:

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{173}$.

Endomorphism algebra over $\F_{173}$
The isogeny class factors as 1.173.az 2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-67}) \)$)$

Base change

This is a primitive isogeny class.

Twists

Below are some of the twists of this isogeny class.

TwistExtension degreeCommon base change
2.173.a_akt$2$(not in LMFDB)
2.173.by_blj$2$(not in LMFDB)
2.173.z_rk$3$(not in LMFDB)

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

TwistExtension degreeCommon base change
2.173.a_akt$2$(not in LMFDB)
2.173.by_blj$2$(not in LMFDB)
2.173.z_rk$3$(not in LMFDB)
2.173.a_kt$4$(not in LMFDB)
2.173.az_rk$6$(not in LMFDB)