Invariants
| Base field: | $\F_{43}$ |
| Dimension: | $2$ |
| L-polynomial: | $1 - 19 x + 172 x^{2} - 817 x^{3} + 1849 x^{4}$ |
| Frobenius angles: | $\pm0.156493675923$, $\pm0.308035816568$ |
| Angle rank: | $2$ (numerical) |
| Number field: | 4.0.1292408.1 |
| Galois group: | $D_{4}$ |
| Jacobians: | $8$ |
| Cyclic group of points: | yes |
This isogeny class is simple and geometrically simple, primitive, not ordinary, and not supersingular. It is principally polarizable and contains a Jacobian.
Newton polygon
| $p$-rank: | $1$ |
| Slopes: | $[0, 1/2, 1/2, 1]$ |
Point counts
Point counts of the abelian variety
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $1186$ | $3389588$ | $6360769432$ | $11702511894944$ | $21613798079898526$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $25$ | $1833$ | $80002$ | $3422985$ | $147024195$ | $6321377874$ | $271818687697$ | $11688204317265$ | $502592658504742$ | $21611482538415913$ |
Jacobians and polarizations
This isogeny class is principally polarizable and contains the Jacobians of 8 curves (of which all are hyperelliptic):
- $y^2=7 x^6+28 x^5+18 x^4+18 x^3+18 x^2+4 x+12$
- $y^2=34 x^6+40 x^5+7 x^4+32 x^3+39 x^2+31 x+26$
- $y^2=32 x^6+29 x^5+34 x^4+x^3+6 x^2+34 x+26$
- $y^2=20 x^6+18 x^5+8 x^4+8 x^3+9 x^2+35 x+8$
- $y^2=10 x^6+7 x^5+4 x^4+31 x^3+21 x^2+34 x+40$
- $y^2=27 x^6+9 x^5+13 x^4+25 x^3+17 x^2+35 x+3$
- $y^2=34 x^6+6 x^5+16 x^4+28 x^3+16 x^2+5$
- $y^2=30 x^6+31 x^5+31 x^4+32 x^3+3 x^2+38 x+1$
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 4.0.1292408.1. |
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.t_gq | $2$ | (not in LMFDB) |