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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $22201$ | $879181801$ | $26781328804624$ | $802326964224789481$ | $24013810603530039138961$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $124$ | $29372$ | $5172418$ | $895709076$ | $154963909844$ | $26808759997958$ | $4637914490027348$ | $802359181412295268$ | $138808137921470311114$ | $24013807853230645957772$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 3 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=105x^6+51x^5+148x^4+150x^3+6x^2+163x+163$
- $y^2=26x^6+137x^5+115x^4+13x^3+145x^2+119x+55$
- $y^2=125x^6+57x^5+92x^4+85x^3+25x^2+x+170$
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.