Invariants
| Base field: | $\F_{173}$ |
| Dimension: | $2$ |
| L-polynomial: | $( 1 - 23 x + 173 x^{2} )^{2}$ |
| $1 - 46 x + 875 x^{2} - 7958 x^{3} + 29929 x^{4}$ | |
| Frobenius angles: | $\pm0.161302001611$, $\pm0.161302001611$ |
| Angle rank: | $1$ (numerical) |
| Jacobians: | $7$ |
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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $22801$ | $884884009$ | $26806381990144$ | $802406420764930921$ | $24014008152537131333641$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $128$ | $29564$ | $5177258$ | $895797780$ | $154965184648$ | $26808773937158$ | $4637914576756120$ | $802359180668423524$ | $138808137883484776274$ | $24013807852395455567564$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 7 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=144x^6+65x^5+123x^4+7x^3+69x^2+75x+138$
- $y^2=116x^6+60x^5+24x^4+80x^3+166x^2+126x+69$
- $y^2=89x^6+68x^5+76x^4+38x^3+138x^2+36x+73$
- $y^2=17x^6+25x^5+70x^4+119x^3+91x^2+79x+85$
- $y^2=10x^6+124x^5+129x^4+168x^3+37x^2+94x+21$
- $y^2=36x^6+149x^5+20x^4+118x^3+123x^2+65x+66$
- $y^2=9x^6+56x^5+112x^4+40x^3+26x^2+160x+118$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{173}$.
Endomorphism algebra over $\F_{173}$| The isogeny class factors as 1.173.ax 2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-163}) \)$)$ |
Base change
This is a primitive isogeny class.