Invariants
| Base field: | $\F_{79}$ |
| Dimension: | $2$ |
| L-polynomial: | $1 - 155 x^{2} + 6241 x^{4}$ |
| Frobenius angles: | $\pm0.0310639581773$, $\pm0.968936041823$ |
| Angle rank: | $1$ (numerical) |
| Number field: | \(\Q(\sqrt{-3}, \sqrt{313})\) |
| Galois group: | $C_2^2$ |
| Jacobians: | $4$ |
| Isomorphism classes: | 8 |
| Cyclic group of points: | yes |
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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $6087$ | $37051569$ | $243086633712$ | $1516209819454521$ | $9468276079177956927$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $80$ | $5932$ | $493040$ | $38926996$ | $3077056400$ | $243085811902$ | $19203908986160$ | $1517108699225188$ | $119851595982618320$ | $9468276075729066652$ |
Jacobians and polarizations
This isogeny class is principally polarizable and contains the Jacobians of 4 curves (of which all are hyperelliptic):
- $y^2=x^6+47 x^3+17$
- $y^2=x^6+63 x^3+12$
- $y^2=x^6+54 x^3+17$
- $y^2=x^6+x^3+57$
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 \(\Q(\sqrt{-3}, \sqrt{313})\). |
| The base change of $A$ to $\F_{79^{2}}$ is 1.6241.afz 2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-939}) \)$)$ |
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 |
|---|---|---|
| 2.79.ad_de | $3$ | (not in LMFDB) |
| 2.79.d_de | $3$ | (not in LMFDB) |
| 2.79.a_fz | $4$ | (not in LMFDB) |