Invariants
| Base field: | $\F_{43}$ |
| Dimension: | $2$ |
| L-polynomial: | $1 - 20 x + 181 x^{2} - 860 x^{3} + 1849 x^{4}$ |
| Frobenius angles: | $\pm0.117188704887$, $\pm0.298340802765$ |
| Angle rank: | $2$ (numerical) |
| Number field: | 4.0.62225.1 |
| Galois group: | $D_{4}$ |
| Jacobians: | $8$ |
| Cyclic group of points: | yes |
This isogeny class is simple and geometrically 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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $1151$ | $3350561$ | $6343649024$ | $11697347891321$ | $21612526371340911$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $24$ | $1812$ | $79788$ | $3421476$ | $147015544$ | $6321332118$ | $271818489288$ | $11688204601668$ | $502592680738164$ | $21611482859082772$ |
Jacobians and polarizations
This isogeny class is principally polarizable and contains the Jacobians of 8 curves (of which all are hyperelliptic):
- $y^2=18 x^6+2 x^5+9 x^4+20 x^3+x^2+26 x+4$
- $y^2=42 x^6+31 x^5+13 x^4+21 x^3+16 x^2+38 x+8$
- $y^2=26 x^6+41 x^5+9 x^4+20 x^3+34 x^2+25 x+39$
- $y^2=7 x^6+28 x^5+x^3+23 x^2+31 x+26$
- $y^2=26 x^6+10 x^5+31 x^4+29 x^3+12 x^2+22 x+18$
- $y^2=25 x^6+27 x^5+10 x^4+10 x^3+25 x^2+19 x+33$
- $y^2=33 x^6+12 x^5+15 x^4+12 x^3+34 x^2+28 x+2$
- $y^2=9 x^6+24 x^5+10 x^4+3 x^3+9 x^2+37 x+20$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{43}$.
Endomorphism algebra over $\F_{43}$| The endomorphism algebra of this simple isogeny class is 4.0.62225.1. |
Base change
This is a primitive isogeny class.
Twists
Below is a list of all twists of this isogeny class.
| Twist | Extension degree | Common base change |
|---|---|---|
| 2.43.u_gz | $2$ | (not in LMFDB) |