Invariants
| Base field: | $\F_{79}$ |
| Dimension: | $1$ |
| L-polynomial: | $1 - x + 79 x^{2}$ |
| Frobenius angles: | $\pm0.482084212174$ |
| Angle rank: | $1$ (numerical) |
| Number field: | \(\Q(\sqrt{-35}) \) |
| Galois group: | $C_2$ |
| Jacobians: | $6$ |
| Isomorphism classes: | 6 |
| 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: | $1$ |
| Slopes: | $[0, 1]$ |
Point counts
Point counts of the abelian variety
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $79$ | $6399$ | $493276$ | $38937915$ | $3077025589$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $79$ | $6399$ | $493276$ | $38937915$ | $3077025589$ | $243088385904$ | $19203912350611$ | $1517108739770835$ | $119851595646690964$ | $9468276087831642279$ |
Jacobians and polarizations
This isogeny class is principally polarizable and contains the Jacobians of 6 curves (of which 0 are hyperelliptic):
- $y^2=x^3+73 x+61$
- $y^2=x^3+34 x+23$
- $y^2=x^3+62 x+28$
- $y^2=x^3+27 x+27$
- $y^2=x^3+28 x+5$
- $y^2=x^3+2 x+6$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{79}$.
Endomorphism algebra over $\F_{79}$| The endomorphism algebra of this simple isogeny class is \(\Q(\sqrt{-35}) \). |
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 |
|---|---|---|
| 1.79.b | $2$ | (not in LMFDB) |