Invariants
| Base field: | $\F_{43}$ |
| Dimension: | $2$ |
| L-polynomial: | $( 1 - 13 x + 43 x^{2} )( 1 - 7 x + 43 x^{2} )$ |
| $1 - 20 x + 177 x^{2} - 860 x^{3} + 1849 x^{4}$ | |
| Frobenius angles: | $\pm0.0421616081610$, $\pm0.320784221581$ |
| Angle rank: | $2$ (numerical) |
| Jacobians: | $6$ |
| Cyclic group of points: | yes |
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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $1147$ | $3334329$ | $6324411184$ | $11685252676041$ | $21607528228877107$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $24$ | $1804$ | $79548$ | $3417940$ | $146981544$ | $6321097078$ | $271817237688$ | $11688198346084$ | $502592637404004$ | $21611482475147164$ |
Jacobians and polarizations
This isogeny class is principally polarizable and contains the Jacobians of 6 curves (of which all are hyperelliptic):
- $y^2=11 x^6+42 x^5+7 x^4+36 x^3+20 x^2+5 x+21$
- $y^2=26 x^6+30 x^5+31 x^4+42 x^3+14 x^2+5 x+26$
- $y^2=7 x^6+27 x^5+20 x^4+41 x^3+24 x^2+14 x+41$
- $y^2=28 x^6+23 x^5+13 x^4+28 x^3+9 x^2+35 x+5$
- $y^2=10 x^6+35 x^5+8 x^4+13 x^3+32 x^2+19 x+11$
- $y^2=7 x^6+12 x^5+11 x^4+8 x^3+39 x^2+26 x+11$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{43}$.
Endomorphism algebra over $\F_{43}$| The isogeny class factors as 1.43.an $\times$ 1.43.ah and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is: |
Base change
This is a primitive isogeny class.