Invariants
| Base field: | $\F_{43}$ |
| Dimension: | $1$ |
| L-polynomial: | $1 - 4 x + 43 x^{2}$ |
| Frobenius angles: | $\pm0.401344489543$ |
| Angle rank: | $1$ (numerical) |
| Number field: | \(\Q(\sqrt{-39}) \) |
| Galois group: | $C_2$ |
| Jacobians: | $8$ |
| Isomorphism classes: | 8 |
| 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: | $1$ |
| Slopes: | $[0, 1]$ |
Point counts
Point counts of the abelian variety
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $40$ | $1920$ | $79960$ | $3417600$ | $146984200$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $40$ | $1920$ | $79960$ | $3417600$ | $146984200$ | $6321317760$ | $271819472440$ | $11688205670400$ | $502592596470760$ | $21611482019529600$ |
Jacobians and polarizations
This isogeny class is principally polarizable and contains the Jacobians of 8 curves (of which 0 are hyperelliptic):
- $y^2=x^3+26 x+26$
- $y^2=x^3+31 x+19$
- $y^2=x^3+41 x+39$
- $y^2=x^3+11 x+11$
- $y^2=x^3+15 x+15$
- $y^2=x^3+5 x+10$
- $y^2=x^3+36 x+36$
- $y^2=x^3+26 x+9$
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 \(\Q(\sqrt{-39}) \). |
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 |
|---|---|---|
| 1.43.e | $2$ | (not in LMFDB) |