Invariants
| Base field: | $\F_{347}$ |
| Dimension: | $1$ |
| L-polynomial: | $1 - 16 x + 347 x^{2}$ |
| Frobenius angles: | $\pm0.358703033405$ |
| Angle rank: | $1$ (numerical) |
| Number field: | \(\Q(\sqrt{-283}) \) |
| Galois group: | $C_2$ |
| Jacobians: | $12$ |
| Isomorphism classes: | 12 |
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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $332$ | $120848$ | $41794484$ | $14498376256$ | $5030915991772$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $332$ | $120848$ | $41794484$ | $14498376256$ | $5030915991772$ | $1745729015388176$ | $605767994136938692$ | $210201493973587054848$ | $72939918400012174334828$ | $25310151684660263897844368$ |
Jacobians and polarizations
This isogeny class is principally polarizable and contains the Jacobians of 12 curves (of which 0 are hyperelliptic):
- $y^2=x^3+105 x+105$
- $y^2=x^3+336 x+325$
- $y^2=x^3+315 x+283$
- $y^2=x^3+96 x+96$
- $y^2=x^3+79 x+158$
- $y^2=x^3+194 x+194$
- $y^2=x^3+39 x+78$
- $y^2=x^3+292 x+237$
- $y^2=x^3+263 x+263$
- $y^2=x^3+x+1$
- $y^2=x^3+231 x+115$
- $y^2=x^3+196 x+196$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{347}$.
Endomorphism algebra over $\F_{347}$| The endomorphism algebra of this simple isogeny class is \(\Q(\sqrt{-283}) \). |
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 |
|---|---|---|
| 1.347.q | $2$ | (not in LMFDB) |