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: | $\pm0.259258415261$, $\pm0.259258415261$ |
| Angle rank: | $1$ (numerical) |
| Jacobians: | $9$ |
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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $1225$ | $3441025$ | $6390403600$ | $11713335125625$ | $21615740475555625$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $26$ | $1860$ | $80372$ | $3426148$ | $147037406$ | $6321307830$ | $271816868762$ | $11688186970948$ | $502592567097836$ | $21611482481919300$ |
Jacobians and polarizations
This isogeny class is principally polarizable and contains the Jacobians of 9 curves (of which all are hyperelliptic):
- $y^2=6 x^6+42 x^5+29 x^4+14 x^3+35 x^2+25$
- $y^2=31 x^6+35 x^4+38 x^3+35 x^2+31$
- $y^2=32 x^6+25 x^5+28 x^4+39 x^3+28 x^2+25 x+32$
- $y^2=20 x^6+14 x^5+40 x^4+40 x^2+14 x+20$
- $y^2=40 x^6+42 x^5+37 x^4+31 x^3+37 x^2+42 x+40$
- $y^2=14 x^6+4 x^5+31 x^4+16 x^3+28 x^2+23 x+26$
- $y^2=8 x^6+21 x^5+36 x^4+22 x^3+4 x^2+4 x+33$
- $y^2=30 x^6+15 x^5+9 x^4+8 x^3+38 x^2+16 x+42$
- $y^2=12 x^6+18 x^5+2 x^4+33 x^3+2 x^2+18 x+12$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{43}$.
Endomorphism algebra over $\F_{43}$| The isogeny class factors as 1.43.aj 2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-91}) \)$)$ |
Base change
This is a primitive isogeny class.