Invariants
| Base field: | $\F_{43}$ |
| Dimension: | $2$ |
| L-polynomial: | $1 + 9 x + 102 x^{2} + 387 x^{3} + 1849 x^{4}$ |
| Frobenius angles: | $\pm0.559529721040$, $\pm0.666781984227$ |
| Angle rank: | $2$ (numerical) |
| Number field: | \(\Q(\sqrt{-590 +18 \sqrt{17}})\) |
| Galois group: | $D_{4}$ |
| Jacobians: | $24$ |
| Cyclic group of points: | no |
| Non-cyclic primes: | $2$ |
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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $2348$ | $3653488$ | $6252996368$ | $11685272177344$ | $21616128162961988$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $53$ | $1973$ | $78644$ | $3417945$ | $147040043$ | $6321273014$ | $271818127529$ | $11688203169265$ | $502592611654316$ | $21611482374499013$ |
Jacobians and polarizations
This isogeny class is principally polarizable and contains the Jacobians of 24 curves (of which all are hyperelliptic):
- $y^2=24 x^6+21 x^5+14 x^4+28 x^3+23 x^2+9 x+9$
- $y^2=20 x^6+23 x^5+24 x^4+15 x^3+22 x^2+37 x+31$
- $y^2=20 x^6+32 x^5+5 x^4+10 x^3+2 x^2+6 x+3$
- $y^2=32 x^6+37 x^5+6 x^4+9 x^3+8 x^2+36 x+21$
- $y^2=21 x^6+25 x^5+29 x^4+28 x^3+23 x^2+24 x+22$
- $y^2=25 x^6+38 x^5+24 x^4+13 x^3+16 x^2+21 x+4$
- $y^2=12 x^6+29 x^5+15 x^4+10 x^3+9 x^2+19 x+32$
- $y^2=40 x^6+28 x^5+38 x^4+42 x^3+33 x^2+20 x+18$
- $y^2=36 x^6+5 x^5+11 x^3+8 x^2+13 x+9$
- $y^2=21 x^6+35 x^5+25 x^4+13 x^3+27 x^2+30 x+36$
- $y^2=23 x^6+20 x^5+18 x^4+40 x^3+41 x^2+28 x+36$
- $y^2=7 x^5+14 x^4+15 x^3+34 x^2+15 x+16$
- $y^2=39 x^6+27 x^5+35 x^4+6 x^3+2 x^2+x$
- $y^2=38 x^6+6 x^5+6 x^4+15 x^3+34 x^2+9 x+23$
- $y^2=36 x^6+10 x^5+20 x^4+13 x^3+20 x^2+27 x+35$
- $y^2=36 x^6+7 x^5+13 x^4+11 x^3+23 x^2+12 x$
- $y^2=33 x^6+19 x^5+42 x^4+25 x^3+12 x^2+38 x$
- $y^2=6 x^6+39 x^5+2 x^4+30 x^3+4 x^2+15 x+32$
- $y^2=35 x^6+31 x^5+21 x^4+2 x^3+18 x^2+23 x+12$
- $y^2=4 x^6+18 x^5+21 x^4+26 x^3+9 x^2+5 x+32$
- $y^2=7 x^6+18 x^5+15 x^4+31 x^3+37 x^2+8 x+11$
- $y^2=14 x^6+33 x^5+16 x^4+8 x^3+10 x^2+36 x+5$
- $y^2=14 x^6+35 x^5+17 x^4+7 x^3+7 x^2+42 x+27$
- $y^2=35 x^6+32 x^5+23 x^4+12 x^3+18 x^2+35$
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 \(\Q(\sqrt{-590 +18 \sqrt{17}})\). |
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.aj_dy | $2$ | (not in LMFDB) |