Invariants
| Base field: | $\F_{43}$ |
| Dimension: | $2$ |
| L-polynomial: | $1 - 18 x + 154 x^{2} - 774 x^{3} + 1849 x^{4}$ |
| Frobenius angles: | $\pm0.0890013239985$, $\pm0.365066878508$ |
| Angle rank: | $2$ (numerical) |
| Number field: | 4.0.316368.2 |
| Galois group: | $C_4$ |
| 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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $1212$ | $3388752$ | $6334199244$ | $11684254235904$ | $21607828357647372$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $26$ | $1834$ | $79670$ | $3417646$ | $146983586$ | $6321248602$ | $271819184894$ | $11688211128094$ | $502592676262346$ | $21611482455892234$ |
Jacobians and polarizations
This isogeny class is principally polarizable and contains the Jacobians of 24 curves (of which all are hyperelliptic):
- $y^2=4 x^6+36 x^5+35 x^4+33 x^3+8 x^2+8 x+42$
- $y^2=2 x^6+6 x^5+35 x^4+37 x^3+2 x^2+10 x+33$
- $y^2=20 x^6+25 x^5+x^4+8 x^3+4 x^2+37 x+20$
- $y^2=5 x^6+12 x^5+2 x^4+26 x^3+8 x^2+15 x+19$
- $y^2=5 x^6+36 x^5+2 x^4+21 x^3+33 x^2+16 x+35$
- $y^2=35 x^5+12 x^4+17 x^3+19 x^2+3 x+8$
- $y^2=37 x^6+26 x^5+19 x^4+31 x^3+28 x^2+39 x+42$
- $y^2=20 x^6+36 x^5+40 x^4+36 x^3+37 x^2+8 x+10$
- $y^2=22 x^6+3 x^5+31 x^4+14 x^3+2 x^2+35 x+12$
- $y^2=15 x^6+37 x^5+40 x^4+22 x^3+30 x^2+8 x+5$
- $y^2=27 x^6+38 x^5+18 x^4+30 x^3+40 x+38$
- $y^2=30 x^6+7 x^5+32 x^4+38 x^3+9 x^2+10 x+15$
- $y^2=33 x^6+11 x^5+23 x^4+42 x^3+40 x^2+21 x+12$
- $y^2=17 x^6+34 x^5+5 x^4+5 x^3+27 x^2+14 x+39$
- $y^2=34 x^6+14 x^5+4 x^4+28 x^3+28 x^2+x+25$
- $y^2=27 x^6+5 x^5+9 x^4+33 x^3+5 x^2+28 x+42$
- $y^2=28 x^6+11 x^5+x^4+18 x^3+10 x^2+25 x+30$
- $y^2=29 x^6+31 x^5+35 x^4+19 x^3+7 x^2+11 x+36$
- $y^2=26 x^6+22 x^5+18 x^4+x^3+x^2+23 x+35$
- $y^2=20 x^6+4 x^5+31 x^4+24 x^3+3 x^2+18 x+32$
- $y^2=18 x^6+22 x^5+17 x^4+16 x^3+23 x^2+2 x$
- $y^2=21 x^5+16 x^4+35 x^3+17 x^2+11 x+34$
- $y^2=27 x^6+35 x^5+16 x^4+35 x^3+23 x^2+11 x+22$
- $y^2=12 x^6+25 x^5+40 x^4+24 x^3+9 x^2+9 x+22$
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 4.0.316368.2. |
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_fy | $2$ | (not in LMFDB) |