Invariants
| Base field: | $\F_{23}$ |
| Dimension: | $2$ |
| L-polynomial: | $( 1 - 6 x + 23 x^{2} )^{2}$ |
| $1 - 12 x + 82 x^{2} - 276 x^{3} + 529 x^{4}$ | |
| Frobenius angles: | $\pm0.284877382774$, $\pm0.284877382774$ |
| Angle rank: | $1$ (numerical) |
| Jacobians: | $14$ |
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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $324$ | $291600$ | $152917956$ | $78848640000$ | $41441895501444$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $12$ | $550$ | $12564$ | $281758$ | $6438732$ | $148006150$ | $3404592084$ | $78310269118$ | $1801153731852$ | $41426534107750$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 14 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=11x^6+2x^4+17x^3+2x^2+11$
- $y^2=11x^6+8x^5+8x^4+8x^2+8x+11$
- $y^2=22x^6+20x^4+7x^3+20x^2+22$
- $y^2=22x^6+2x^5+20x^4+3x^3+22x^2+13x+17$
- $y^2=16x^6+6x^4+6x^2+16$
- $y^2=19x^6+5x^4+5x^2+19$
- $y^2=22x^6+7x^4+22x^3+7x^2+22$
- $y^2=x^6+7x^5+12x^4+12x^3+6x^2+19x+3$
- $y^2=16x^5+3x^4+4x^3+3x^2+16x$
- $y^2=5x^6+16x^5+9x^4+16x^3+9x^2+16x+5$
- $y^2=18x^6+12x^5+5x^4+8x^3+10x^2+2x+6$
- $y^2=7x^6+18x^5+x^4+4x^3+9x^2+9x+20$
- $y^2=9x^6+17x^5+6x^4+22x^3+8x^2+20x+6$
- $y^2=10x^6+11x^5+22x^4+5x^2+22x+15$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{23}$.
Endomorphism algebra over $\F_{23}$| The isogeny class factors as 1.23.ag 2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-14}) \)$)$ |
Base change
This is a primitive isogeny class.