Invariants
| Base field: | $\F_{43}$ |
| Dimension: | $2$ |
| L-polynomial: | $1 - 4 x + 83 x^{2} - 172 x^{3} + 1849 x^{4}$ |
| Frobenius angles: | $\pm0.384741223030$, $\pm0.515679306135$ |
| Angle rank: | $2$ (numerical) |
| Number field: | 4.0.20234256.1 |
| Galois group: | $D_{4}$ |
| Jacobians: | $24$ |
| 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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $1757$ | $3705513$ | $6354555956$ | $11674266878169$ | $21608888651046557$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $40$ | $2000$ | $79924$ | $3414724$ | $146990800$ | $6321425150$ | $271818853360$ | $11688200597764$ | $502592636415532$ | $21611482311470000$ |
Jacobians and polarizations
This isogeny class is principally polarizable and contains the Jacobians of 24 curves (of which all are hyperelliptic):
- $y^2=2 x^6+42 x^5+28 x^4+19 x^3+x^2+30 x+1$
- $y^2=30 x^6+35 x^5+3 x^4+9 x^3+42 x^2+3 x+27$
- $y^2=19 x^6+4 x^5+9 x^4+33 x^3+6 x^2+38 x+34$
- $y^2=9 x^6+7 x^5+24 x^4+17 x^3+23 x^2+28 x+41$
- $y^2=39 x^6+35 x^5+4 x^4+31 x^3+18 x^2+3 x+29$
- $y^2=7 x^6+15 x^5+29 x^4+27 x^3+18 x^2+42 x+27$
- $y^2=34 x^6+7 x^5+31 x^4+10 x^3+31 x^2+8 x+5$
- $y^2=7 x^6+16 x^5+14 x^4+42 x^3+35 x^2+15 x+11$
- $y^2=20 x^6+39 x^4+39 x^3+37 x^2+25 x+32$
- $y^2=42 x^6+3 x^5+17 x^3+x+8$
- $y^2=4 x^6+5 x^5+6 x^4+21 x^3+30 x^2+12 x+1$
- $y^2=4 x^6+24 x^5+41 x^4+11 x^3+4 x^2+5 x+20$
- $y^2=29 x^6+31 x^5+9 x^4+34 x^3+37 x^2+35 x+34$
- $y^2=23 x^6+24 x^5+32 x^4+14 x^3+32 x^2+30 x+29$
- $y^2=8 x^6+21 x^5+5 x^4+5 x^3+12 x^2+25 x+39$
- $y^2=34 x^6+21 x^5+38 x^4+31 x^3+11 x^2+16 x+22$
- $y^2=36 x^6+36 x^5+41 x^4+34 x^3+2 x^2+28 x+39$
- $y^2=24 x^6+33 x^5+2 x^4+42 x^3+33 x^2+37 x+28$
- $y^2=37 x^6+36 x^5+25 x^4+12 x^3+25 x^2+39 x+10$
- $y^2=42 x^6+40 x^5+21 x^4+39 x^3+24 x^2+12 x+30$
- $y^2=12 x^6+26 x^5+7 x^4+26 x^3+4 x^2+11 x+7$
- $y^2=5 x^6+31 x^5+10 x^4+34 x^3+11 x^2+5 x+4$
- $y^2=10 x^6+7 x^5+5 x^4+37 x^3+41 x^2+41 x+10$
- $y^2=12 x^6+32 x^5+2 x^4+24 x^3+15 x^2+20 x+38$
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 4.0.20234256.1. |
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.e_df | $2$ | (not in LMFDB) |