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: | $\pm0.776024765496$, $\pm0.776024765496$ |
| Angle rank: | $1$ (numerical) |
| Jacobians: | $11$ |
| Cyclic group of points: | no |
| Non-cyclic primes: | $2, 3$ |
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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $2916$ | $3370896$ | $6275491524$ | $11712164668416$ | $21604853034979236$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $64$ | $1822$ | $78928$ | $3425806$ | $146963344$ | $6321512878$ | $271819052128$ | $11688189424798$ | $502592701501024$ | $21611481884313022$ |
Jacobians and polarizations
This isogeny class is principally polarizable and contains the Jacobians of 11 curves (of which all are hyperelliptic):
- $y^2=x^6+x^3+35$
- $y^2=17 x^6+25 x^4+25 x^2+17$
- $y^2=7 x^5+10 x^4+15 x^3+10 x^2+7 x$
- $y^2=40 x^6+10 x^5+24 x^4+13 x^3+24 x^2+10 x+40$
- $y^2=x^6+3 x^5+18 x^4+x^3+28 x^2+35 x+24$
- $y^2=32 x^6+17 x^5+34 x^4+7 x^3+22 x^2+40 x+2$
- $y^2=13 x^6+11 x^5+37 x^4+7 x^3+26 x^2+7 x+16$
- $y^2=25 x^6+17 x^5+22 x^4+22 x^2+17 x+25$
- $y^2=x^6+30 x^5+38 x^4+38 x^2+13 x+1$
- $y^2=x^6+17 x^3+11$
- $y^2=8 x^5+21 x^4+9 x^3+39 x^2+39 x+41$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{43}$.
Endomorphism algebra over $\F_{43}$| The isogeny class factors as 1.43.k 2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-2}) \)$)$ |
Base change
This is a primitive isogeny class.