Invariants
| Base field: | $\F_{43}$ |
| Dimension: | $2$ |
| L-polynomial: | $1 - 68 x^{2} + 1849 x^{4}$ |
| Frobenius angles: | $\pm0.104859005203$, $\pm0.895140994797$ |
| Angle rank: | $1$ (numerical) |
| Number field: | \(\Q(\sqrt{-2}, \sqrt{-77})\) |
| Galois group: | $C_2^2$ |
| Jacobians: | $24$ |
| Isomorphism classes: | 72 |
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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $1782$ | $3175524$ | $6321425814$ | $11681876351376$ | $21611482603882182$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $44$ | $1714$ | $79508$ | $3416950$ | $147008444$ | $6321488578$ | $271818611108$ | $11688212237854$ | $502592611936844$ | $21611482894480114$ |
Jacobians and polarizations
This isogeny class is principally polarizable and contains the Jacobians of 24 curves (of which all are hyperelliptic):
- $y^2=22 x^6+31 x^5+37 x^4+35 x^3+11 x^2+14 x+42$
- $y^2=23 x^6+7 x^5+25 x^4+19 x^3+33 x^2+42 x+40$
- $y^2=5 x^6+12 x^4+13 x^3+12 x^2+29 x+26$
- $y^2=15 x^6+36 x^4+39 x^3+36 x^2+x+35$
- $y^2=9 x^6+24 x^5+5 x^4+27 x^3+7 x^2+6 x+25$
- $y^2=27 x^6+29 x^5+15 x^4+38 x^3+21 x^2+18 x+32$
- $y^2=20 x^6+23 x^5+10 x^4+5 x^3+9 x^2+9 x+35$
- $y^2=17 x^6+26 x^5+30 x^4+15 x^3+27 x^2+27 x+19$
- $y^2=30 x^6+28 x^5+34 x^4+14 x^3+11 x^2+3 x+29$
- $y^2=4 x^6+41 x^5+16 x^4+42 x^3+33 x^2+9 x+1$
- $y^2=34 x^6+16 x^5+15 x^4+6 x^3+33 x^2+30 x+8$
- $y^2=16 x^6+5 x^5+2 x^4+18 x^3+13 x^2+4 x+24$
- $y^2=28 x^6+38 x^5+25 x^4+8 x^3+18 x^2+41 x+7$
- $y^2=41 x^6+28 x^5+32 x^4+24 x^3+11 x^2+37 x+21$
- $y^2=41 x^6+40 x^5+36 x^4+22 x^3+40 x^2+6 x+22$
- $y^2=37 x^6+34 x^5+22 x^4+23 x^3+34 x^2+18 x+23$
- $y^2=6 x^6+27 x^5+38 x^4+19 x^3+22 x^2+20 x+17$
- $y^2=18 x^6+38 x^5+28 x^4+14 x^3+23 x^2+17 x+8$
- $y^2=39 x^6+42 x^5+9 x^4+3 x^3+33 x^2+5 x+18$
- $y^2=31 x^6+40 x^5+27 x^4+9 x^3+13 x^2+15 x+11$
- $y^2=21 x^6+22 x^5+30 x^4+27 x^3+27 x^2+3 x+19$
- $y^2=20 x^6+23 x^5+4 x^4+38 x^3+38 x^2+9 x+14$
- $y^2=35 x^6+9 x^5+6 x^4+34 x^3+9 x^2+34 x+30$
- $y^2=19 x^6+27 x^5+18 x^4+16 x^3+27 x^2+16 x+4$
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 \(\Q(\sqrt{-2}, \sqrt{-77})\). |
| The base change of $A$ to $\F_{43^{2}}$ is 1.1849.acq 2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-77}) \)$)$ |
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.a_cq | $4$ | (not in LMFDB) |
| 2.43.ag_s | $8$ | (not in LMFDB) |
| 2.43.g_s | $8$ | (not in LMFDB) |