Invariants
| Base field: | $\F_{79}$ |
| Dimension: | $1$ |
| L-polynomial: | $1 + 79 x^{2}$ |
| Frobenius angles: | $\pm0.5$ |
| Angle rank: | $0$ (numerical) |
| Number field: | \(\Q(\sqrt{-79}) \) |
| Galois group: | $C_2$ |
| Jacobians: | $10$ |
| Isomorphism classes: | 10 |
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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $80$ | $6400$ | $493040$ | $38937600$ | $3077056400$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $80$ | $6400$ | $493040$ | $38937600$ | $3077056400$ | $243088441600$ | $19203908986160$ | $1517108732006400$ | $119851595982618320$ | $9468276088780960000$ |
Jacobians and polarizations
This isogeny class is principally polarizable and contains the Jacobians of 10 curves (of which 0 are hyperelliptic):
- $y^2=x^3+39 x+39$
- $y^2=x^3+21 x+63$
- $y^2=x^3+35 x+26$
- $y^2=x^3+19 x+19$
- $y^2=x^3+13 x+39$
- $y^2=x^3+3 x$
- $y^2=x^3+7 x+21$
- $y^2=x^3+55 x+55$
- $y^2=x^3+71 x+71$
- $y^2=x^3+x$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{79^{2}}$.
Endomorphism algebra over $\F_{79}$| The endomorphism algebra of this simple isogeny class is \(\Q(\sqrt{-79}) \). |
| The base change of $A$ to $\F_{79^{2}}$ is the simple isogeny class 1.6241.gc and its endomorphism algebra is the quaternion algebra over \(\Q\) ramified at $79$ and $\infty$. |
Base change
This is a primitive isogeny class.
Twists
This isogeny class has no twists.