Invariants
| Base field: | $\F_{43}$ |
| Dimension: | $1$ |
| L-polynomial: | $1 + 43 x^{2}$ |
| Frobenius angles: | $\pm0.5$ |
| Angle rank: | $0$ (numerical) |
| Number field: | \(\Q(\sqrt{-43}) \) |
| Galois group: | $C_2$ |
| Jacobians: | $4$ |
| Isomorphism classes: | 4 |
This isogeny class is simple and geometrically simple, primitive, not ordinary, and supersingular. It is principally polarizable and contains a Jacobian.
Newton polygon
This isogeny class is supersingular.
| $p$-rank: | $0$ |
| Slopes: | $[1/2, 1/2]$ |
Point counts
Point counts of the abelian variety
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $44$ | $1936$ | $79508$ | $3415104$ | $147008444$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $44$ | $1936$ | $79508$ | $3415104$ | $147008444$ | $6321522064$ | $271818611108$ | $11688193440000$ | $502592611936844$ | $21611482607301136$ |
Jacobians and polarizations
This isogeny class is principally polarizable and contains the Jacobians of 4 curves (of which 0 are hyperelliptic):
- $y^2=x^3+29 x+15$
- $y^2=x^3+18 x+18$
- $y^2=x^3+2 x$
- $y^2=x^3+x$
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 \(\Q(\sqrt{-43}) \). |
| The base change of $A$ to $\F_{43^{2}}$ is the simple isogeny class 1.1849.di and its endomorphism algebra is the quaternion algebra over \(\Q\) ramified at $43$ and $\infty$. |
Base change
This is a primitive isogeny class.
Twists
This isogeny class has no twists.