Invariants
| Base field: | $\F_{43}$ |
| Dimension: | $2$ |
| L-polynomial: | $1 - 21 x + 193 x^{2} - 903 x^{3} + 1849 x^{4}$ |
| Frobenius angles: | $\pm0.112604323980$, $\pm0.269216105066$ |
| Angle rank: | $2$ (numerical) |
| Number field: | 4.0.336141.1 |
| Galois group: | $D_{4}$ |
| Jacobians: | $8$ |
| 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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $1119$ | $3320073$ | $6336421425$ | $11698519580829$ | $21613841264552304$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $23$ | $1795$ | $79697$ | $3421819$ | $147024488$ | $6321390055$ | $271818456611$ | $11688200730499$ | $502592645985761$ | $21611482751459350$ |
Jacobians and polarizations
This isogeny class is principally polarizable and contains the Jacobians of 8 curves (of which all are hyperelliptic):
- $y^2=32 x^6+30 x^5+23 x^4+17 x^3+19 x^2+5 x+32$
- $y^2=35 x^6+15 x^5+37 x^4+32 x^3+39 x^2+39 x+2$
- $y^2=17 x^6+32 x^5+9 x^4+5 x^3+24 x^2+20 x+24$
- $y^2=9 x^6+x^5+33 x^4+13 x^3+42 x+27$
- $y^2=28 x^6+2 x^5+24 x^4+15 x^3+30 x^2+26$
- $y^2=x^6+9 x^5+21 x^4+37 x^3+40 x^2+21 x+12$
- $y^2=35 x^6+26 x^5+29 x^4+4 x^3+13 x^2+33 x+8$
- $y^2=9 x^6+5 x^5+28 x^4+17 x^3+39 x^2+24 x+3$
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 4.0.336141.1. |
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.v_hl | $2$ | (not in LMFDB) |