Invariants
| Base field: | $\F_{43}$ |
| Dimension: | $2$ |
| L-polynomial: | $1 - 61 x^{2} + 1849 x^{4}$ |
| Frobenius angles: | $\pm0.124505058506$, $\pm0.875494941494$ |
| Angle rank: | $1$ (numerical) |
| Number field: | \(\Q(\zeta_{12})\) |
| Galois group: | $C_2^2$ |
| Jacobians: | $21$ |
| Isomorphism classes: | 29 |
| Cyclic group of points: | yes |
This isogeny class is simple but not 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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $1789$ | $3200521$ | $6321474436$ | $11688049850841$ | $21611482524392989$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $44$ | $1728$ | $79508$ | $3418756$ | $147008444$ | $6321585822$ | $271818611108$ | $11688213951748$ | $502592611936844$ | $21611482735501728$ |
Jacobians and polarizations
This isogeny class is principally polarizable and contains the Jacobians of 21 curves (of which all are hyperelliptic):
- $y^2=2 x^6+14 x^5+11 x^4+12 x^3+34 x^2+21 x+21$
- $y^2=22 x^6+26 x^5+20 x^4+2 x^3+22 x^2+18 x+17$
- $y^2=23 x^6+35 x^5+17 x^4+6 x^3+23 x^2+11 x+8$
- $y^2=6 x^6+35 x^5+32 x^4+5 x^3+11 x^2+21 x+21$
- $y^2=34 x^6+18 x^5+6 x^4+22 x^3+27 x^2+42 x+13$
- $y^2=23 x^6+11 x^5+9 x^4+19 x^3+8 x^2+16 x+15$
- $y^2=8 x^6+2 x^5+11 x^4+37 x^3+31 x^2+16 x+20$
- $y^2=24 x^6+6 x^5+33 x^4+25 x^3+7 x^2+5 x+17$
- $y^2=15 x^6+41 x^5+13 x^4+7 x^3+28 x^2+15 x+14$
- $y^2=39 x^6+11 x^5+28 x^4+12 x^3+12 x^2+10 x+21$
- $y^2=31 x^6+33 x^5+41 x^4+36 x^3+36 x^2+30 x+20$
- $y^2=26 x^6+29 x^5+13 x^4+24 x^3+21 x^2+4 x+10$
- $y^2=38 x^6+15 x^5+27 x^4+31 x^3+7 x^2+20 x+33$
- $y^2=28 x^6+2 x^5+38 x^4+7 x^3+21 x^2+17 x+13$
- $y^2=19 x^6+42 x^5+15 x^4+4 x^3+9 x^2+39 x+17$
- $y^2=14 x^6+40 x^5+2 x^4+12 x^3+27 x^2+31 x+8$
- $y^2=8 x^6+12 x^5+35 x^4+42 x^3+28 x^2+21 x+29$
- $y^2=24 x^6+36 x^5+19 x^4+40 x^3+41 x^2+20 x+1$
- $y^2=29 x^6+36 x^5+17 x^4+3 x^3+23 x^2+x+16$
- $y^2=37 x^6+41 x^5+2 x^4+3 x^3+16 x^2+34 x+36$
- $y^2=25 x^6+37 x^5+6 x^4+9 x^3+5 x^2+16 x+22$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{43^{2}}$.
Endomorphism algebra over $\F_{43}$| The endomorphism algebra of this simple isogeny class is \(\Q(\zeta_{12})\). |
| The base change of $A$ to $\F_{43^{2}}$ is 1.1849.acj 2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-3}) \)$)$ |
Base change
This is a primitive isogeny class.