Invariants
| Base field: | $\F_{23}$ |
| Dimension: | $3$ |
| L-polynomial: | $1 - 9 x + 89 x^{2} - 422 x^{3} + 2047 x^{4} - 4761 x^{5} + 12167 x^{6}$ |
| Frobenius angles: | $\pm0.294192962589$, $\pm0.408795228422$, $\pm0.483043461025$ |
| Angle rank: | $3$ (numerical) |
| Number field: | 6.0.11362414528.1 |
| Galois group: | $S_4\times C_2$ |
| Cyclic group of points: | no |
| Non-cyclic primes: | $2$ |
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: | $3$ |
| Slopes: | $[0, 0, 0, 1, 1, 1]$ |
Point counts
Point counts of the abelian variety
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $9112$ | $177647552$ | $1862584320928$ | $21869900205915136$ | $266391008958707054152$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $15$ | $627$ | $12576$ | $279271$ | $6430445$ | $148037388$ | $3404859123$ | $78310596783$ | $1801151192640$ | $41426522577307$ |
Jacobians and polarizations
This isogeny class is principally polarizable and contains the Jacobians of 15 hyperelliptic curves, but it is unknown how many Jacobians of non-hyperelliptic curves it contains:
- $y^2=22 x^8+10 x^6+19 x^5+15 x^4+16 x^3+4 x^2+13 x$
- $y^2=22 x^8+21 x^7+7 x^6+21 x^5+10 x^4+13 x^2+7 x+21$
- $y^2=22 x^8+8 x^7+13 x^6+12 x^5+x^4+x^3+14 x^2+16 x+10$
- $y^2=x^7+x^6+9 x^5+18 x^4+x^3+20 x^2+9 x+11$
- $y^2=x^7+22 x^6+21 x^5+22 x^4+10 x^3+13 x^2+20 x+15$
- $y^2=x^7+10 x^6+20 x^5+20 x^4+7 x^3+2 x^2+8 x+21$
- $y^2=x^7+3 x^6+x^5+15 x^4+20 x^3+3 x^2+10 x+9$
- $y^2=22 x^7+15 x^6+18 x^5+13 x^3+15 x^2+11 x+8$
- $y^2=x^7+20 x^6+7 x^5+22 x^4+20 x^3+17 x^2+16 x+11$
- $y^2=22 x^8+5 x^7+9 x^6+7 x^5+2 x^4+14 x^3+17 x+20$
- $y^2=22 x^8+x^7+17 x^6+7 x^5+14 x^4+14 x^3+14 x^2+12 x+8$
- $y^2=x^8+3 x^7+18 x^6+4 x^5+15 x^4+15 x^3+7 x^2+13 x+22$
- $y^2=x^8+16 x^7+14 x^6+8 x^5+9 x^4+17 x^3+3 x^2+19 x+17$
- $y^2=x^8+x^7+22 x^6+15 x^5+7 x^4+6 x^3+10 x^2+5 x+21$
- $y^2=22 x^8+4 x^7+12 x^6+7 x^5+x^4+19 x^3+12 x^2+10 x+10$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{23}$.
Endomorphism algebra over $\F_{23}$| The endomorphism algebra of this simple isogeny class is 6.0.11362414528.1. |
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 |
|---|---|---|
| 3.23.j_dl_qg | $2$ | (not in LMFDB) |