Invariants
| Base field: | $\F_{43}$ |
| Dimension: | $2$ |
| L-polynomial: | $( 1 + 9 x + 43 x^{2} )^{2}$ |
| $1 + 18 x + 167 x^{2} + 774 x^{3} + 1849 x^{4}$ | |
| Frobenius angles: | $\pm0.740741584739$, $\pm0.740741584739$ |
| Angle rank: | $1$ (numerical) |
| Jacobians: | $9$ |
| Cyclic group of points: | no |
| Non-cyclic primes: | $53$ |
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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $2809$ | $3441025$ | $6253013776$ | $11713335125625$ | $21607225158445369$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $62$ | $1860$ | $78644$ | $3426148$ | $146979482$ | $6321307830$ | $271820353454$ | $11688186970948$ | $502592656775852$ | $21611482481919300$ |
Jacobians and polarizations
This isogeny class is principally polarizable and contains the Jacobians of 9 curves (of which all are hyperelliptic):
- $y^2=2 x^6+14 x^5+24 x^4+19 x^3+26 x^2+37$
- $y^2=7 x^6+19 x^4+28 x^3+19 x^2+7$
- $y^2=25 x^6+37 x^5+38 x^4+13 x^3+38 x^2+37 x+25$
- $y^2=21 x^6+19 x^5+42 x^4+42 x^2+19 x+21$
- $y^2=34 x^6+40 x^5+25 x^4+7 x^3+25 x^2+40 x+34$
- $y^2=19 x^6+30 x^5+39 x^4+34 x^3+38 x^2+22 x+23$
- $y^2=17 x^6+7 x^5+12 x^4+36 x^3+30 x^2+30 x+11$
- $y^2=10 x^6+5 x^5+3 x^4+17 x^3+27 x^2+34 x+14$
- $y^2=36 x^6+11 x^5+6 x^4+13 x^3+6 x^2+11 x+36$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{43}$.
Endomorphism algebra over $\F_{43}$| The isogeny class factors as 1.43.j 2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-91}) \)$)$ |
Base change
This is a primitive isogeny class.