Invariants
| Base field: | $\F_{43}$ |
| Dimension: | $2$ |
| L-polynomial: | $( 1 - 10 x + 43 x^{2} )^{2}$ |
| $1 - 20 x + 186 x^{2} - 860 x^{3} + 1849 x^{4}$ | |
| Frobenius angles: | $\pm0.223975234504$, $\pm0.223975234504$ |
| Angle rank: | $1$ (numerical) |
| Jacobians: | $11$ |
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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $1156$ | $3370896$ | $6367720804$ | $11712164668416$ | $21618113196628036$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $24$ | $1822$ | $80088$ | $3425806$ | $147053544$ | $6321512878$ | $271818170088$ | $11688189424798$ | $502592522372664$ | $21611481884313022$ |
Jacobians and polarizations
This isogeny class is principally polarizable and contains the Jacobians of 11 curves (of which all are hyperelliptic):
- $y^2=3 x^6+3 x^3+19$
- $y^2=20 x^6+37 x^4+37 x^2+20$
- $y^2=21 x^5+30 x^4+2 x^3+30 x^2+21 x$
- $y^2=42 x^6+32 x^5+8 x^4+33 x^3+8 x^2+32 x+42$
- $y^2=29 x^6+x^5+6 x^4+29 x^3+38 x^2+26 x+8$
- $y^2=10 x^6+8 x^5+16 x^4+21 x^3+23 x^2+34 x+6$
- $y^2=39 x^6+33 x^5+25 x^4+21 x^3+35 x^2+21 x+5$
- $y^2=37 x^6+20 x^5+36 x^4+36 x^2+20 x+37$
- $y^2=3 x^6+4 x^5+28 x^4+28 x^2+39 x+3$
- $y^2=3 x^6+8 x^3+33$
- $y^2=17 x^5+7 x^4+3 x^3+13 x^2+13 x+28$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{43}$.
Endomorphism algebra over $\F_{43}$| The isogeny class factors as 1.43.ak 2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-2}) \)$)$ |
Base change
This is a primitive isogeny class.