Invariants
| Base field: | $\F_{43}$ |
| Dimension: | $2$ |
| L-polynomial: | $( 1 - 11 x + 43 x^{2} )^{2}$ |
| $1 - 22 x + 207 x^{2} - 946 x^{3} + 1849 x^{4}$ | |
| Frobenius angles: | $\pm0.183291501244$, $\pm0.183291501244$ |
| Angle rank: | $1$ (numerical) |
| Jacobians: | $6$ |
| Cyclic group of points: | no |
| Non-cyclic primes: | $3, 11$ |
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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $1089$ | $3294225$ | $6335523216$ | $11705122625625$ | $21618368737250769$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $22$ | $1780$ | $79684$ | $3423748$ | $147055282$ | $6321665590$ | $271819925014$ | $11688201721348$ | $502592571320092$ | $21611481804418900$ |
Jacobians and polarizations
This isogeny class is principally polarizable and contains the Jacobians of 6 curves (of which all are hyperelliptic):
- $y^2=22 x^6+11 x^5+33 x^4+7 x^3+42 x^2+21 x+30$
- $y^2=42 x^6+3 x^5+13 x^4+29 x^3+13 x^2+3 x+42$
- $y^2=7 x^6+25 x^5+14 x^4+15 x^3+14 x^2+25 x+7$
- $y^2=x^6+23 x^3+41$
- $y^2=11 x^6+33 x^5+24 x^4+41 x^3+24 x^2+33 x+11$
- $y^2=42 x^6+31 x^5+30 x^4+34 x^3+30 x^2+31 x+42$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{43}$.
Endomorphism algebra over $\F_{43}$| The isogeny class factors as 1.43.al 2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-51}) \)$)$ |
Base change
This is a primitive isogeny class.