Invariants
| Base field: | $\F_{173}$ |
| Dimension: | $1$ |
| L-polynomial: | $1 + 14 x + 173 x^{2}$ |
| Frobenius angles: | $\pm0.678634614626$ |
| Angle rank: | $1$ (numerical) |
| Number field: | \(\Q(\sqrt{-31}) \) |
| Galois group: | $C_2$ |
| Jacobians: | $12$ |
| Isomorphism classes: | 12 |
This isogeny class is simple and geometrically simple, primitive, ordinary, and not supersingular. It is principally polarizable and contains a Jacobian.
Newton polygon
This isogeny class is ordinary.
| $p$-rank: | $1$ |
| Slopes: | $[0, 1]$ |
Point counts
Point counts of the abelian variety
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $188$ | $30080$ | $5173196$ | $895782400$ | $154964151388$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $188$ | $30080$ | $5173196$ | $895782400$ | $154964151388$ | $26808743239040$ | $4637914422896236$ | $802359178871961600$ | $138808137854136724988$ | $24013807852853642326400$ |
Jacobians and polarizations
This isogeny class is principally polarizable and contains the Jacobians of 12 curves (of which 0 are hyperelliptic):
- $y^2=x^3+165 x+165$
- $y^2=x^3+81 x+81$
- $y^2=x^3+98 x+23$
- $y^2=x^3+41 x+82$
- $y^2=x^3+77 x+154$
- $y^2=x^3+120 x+67$
- $y^2=x^3+17 x+17$
- $y^2=x^3+101 x+101$
- $y^2=x^3+95 x+17$
- $y^2=x^3+89 x+5$
- $y^2=x^3+136 x+99$
- $y^2=x^3+56 x+56$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{173}$.
Endomorphism algebra over $\F_{173}$| The endomorphism algebra of this simple isogeny class is \(\Q(\sqrt{-31}) \). |
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 |
|---|---|---|
| 1.173.ao | $2$ | (not in LMFDB) |