Invariants
| Base field: | $\F_{79}$ |
| Dimension: | $1$ |
| L-polynomial: | $1 - 4 x + 79 x^{2}$ |
| Frobenius angles: | $\pm0.427756044762$ |
| Angle rank: | $1$ (numerical) |
| Number field: | \(\Q(\sqrt{-3}) \) |
| Galois group: | $C_2$ |
| Jacobians: | $10$ |
| Isomorphism classes: | 10 |
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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $76$ | $6384$ | $493924$ | $38942400$ | $3076955836$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $76$ | $6384$ | $493924$ | $38942400$ | $3076955836$ | $243087660144$ | $19203917749204$ | $1517108828793600$ | $119851595365885996$ | $9468276078667841904$ |
Jacobians and polarizations
This isogeny class is principally polarizable and contains the Jacobians of 10 curves (of which 0 are hyperelliptic):
- $y^2=x^3+75 x+67$
- $y^2=x^3+12$
- $y^2=x^3+64 x+64$
- $y^2=x^3+28 x+28$
- $y^2=x^3+58 x+16$
- $y^2=x^3+15 x+15$
- $y^2=x^3+44 x+44$
- $y^2=x^3+14 x+42$
- $y^2=x^3+4 x+12$
- $y^2=x^3+8 x+24$
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 \(\Q(\sqrt{-3}) \). |
Base change
This is a primitive isogeny class.