Properties

Label 2.173.aby_blj
Base Field $\F_{173}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

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

This isogeny class is not simple.

Newton polygon

This isogeny class is ordinary.

$p$-rank:  $2$
Slopes:  $[0, 0, 1, 1]$

Point counts

This isogeny class contains the Jacobians of 3 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 22201 879181801 26781328804624 802326964224789481 24013810603530039138961 718709433924468742544920576 21510250058154373435229667433129 643780253640718644727815368232575625 19267699146964781848315305574009365809296 576662967597000535442693223972804346029302521

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

Decomposition and endomorphism algebra

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

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)