Invariants
| Base field: | $\F_{173}$ |
| Dimension: | $2$ |
| L-polynomial: | $( 1 - 25 x + 173 x^{2} )( 1 - 23 x + 173 x^{2} )$ |
| $1 - 48 x + 921 x^{2} - 8304 x^{3} + 29929 x^{4}$ | |
| Frobenius angles: | $\pm0.100717649571$, $\pm0.161302001611$ |
| Angle rank: | $2$ (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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $22499$ | $882028297$ | $26793852469184$ | $802366691511310249$ | $24013909377830444581499$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $126$ | $29468$ | $5174838$ | $895753428$ | $154964547246$ | $26808766967558$ | $4637914533391734$ | $802359181040359396$ | $138808137902477543694$ | $24013807852813050762668$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 3 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=61x^6+140x^5+42x^4+29x^3+42x^2+140x+61$
- $y^2=162x^6+29x^5+169x^4+118x^3+169x^2+29x+162$
- $y^2=107x^6+82x^5+138x^4+152x^3+138x^2+82x+107$
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 $\times$ 1.173.ax and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is: |
Base change
This is a primitive isogeny class.
Twists
Below is a list of all twists of this isogeny class.
| Twist | Extension degree | Common base change |
|---|---|---|
| 2.173.ac_aiv | $2$ | (not in LMFDB) |
| 2.173.c_aiv | $2$ | (not in LMFDB) |
| 2.173.bw_bjl | $2$ | (not in LMFDB) |