Invariants
| Base field: | $\F_{43}$ |
| Dimension: | $2$ |
| L-polynomial: | $1 - 18 x + 152 x^{2} - 774 x^{3} + 1849 x^{4}$ |
| Frobenius angles: | $\pm0.0612301159281$, $\pm0.372152980887$ |
| Angle rank: | $2$ (numerical) |
| Number field: | \(\Q(\sqrt{-76 -18 \sqrt{15}})\) |
| Galois group: | $D_{4}$ |
| Jacobians: | $16$ |
| 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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $1210$ | $3380740$ | $6325566610$ | $11679577707600$ | $21606214423395250$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $26$ | $1830$ | $79562$ | $3416278$ | $146972606$ | $6321180390$ | $271818717182$ | $11688206879518$ | $502592639533706$ | $21611482226376150$ |
Jacobians and polarizations
This isogeny class is principally polarizable and contains the Jacobians of 16 curves (of which all are hyperelliptic):
- $y^2=40 x^6+23 x^5+13 x^4+23 x^3+36 x^2+30 x+6$
- $y^2=37 x^6+30 x^5+21 x^4+16 x^3+29 x^2+39 x+12$
- $y^2=13 x^6+4 x^5+21 x^3+18 x^2+27 x+12$
- $y^2=22 x^6+2 x^5+39 x^4+19 x^3+16 x^2+12 x+5$
- $y^2=25 x^6+x^5+19 x^4+18 x^3+23 x^2+12 x+27$
- $y^2=22 x^6+41 x^5+28 x^4+21 x^3+25 x^2+40 x+30$
- $y^2=26 x^6+21 x^5+19 x^4+14 x^3+6 x^2+2 x+27$
- $y^2=15 x^6+x^5+39 x^4+27 x^3+14 x^2+38 x+32$
- $y^2=40 x^6+10 x^5+42 x^4+x^3+2 x^2+27 x+19$
- $y^2=27 x^6+31 x^5+21 x^4+16 x^3+20 x^2+11 x+42$
- $y^2=32 x^6+30 x^5+11 x^4+38 x^3+29 x^2+25 x+26$
- $y^2=28 x^6+3 x^5+4 x^4+7 x^3+40 x^2+30 x+5$
- $y^2=38 x^6+25 x^5+30 x^4+33 x^3+39 x^2+17 x+8$
- $y^2=5 x^6+7 x^5+26 x^4+35 x^3+36 x^2+39 x+32$
- $y^2=10 x^5+20 x^4+6 x^3+12 x^2+34$
- $y^2=22 x^6+13 x^5+15 x^4+23 x^3+13 x^2+5 x+3$
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 \(\Q(\sqrt{-76 -18 \sqrt{15}})\). |
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.s_fw | $2$ | (not in LMFDB) |