Invariants
| Base field: | $\F_{347}$ |
| Dimension: | $1$ |
| L-polynomial: | $1 - 3 x + 347 x^{2}$ |
| Frobenius angles: | $\pm0.474340563941$ |
| Angle rank: | $1$ (numerical) |
| Number field: | \(\Q(\sqrt{-1379}) \) |
| Galois group: | $C_2$ |
| Jacobians: | $16$ |
| Isomorphism classes: | 16 |
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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $345$ | $121095$ | $41785020$ | $14498098875$ | $5030917806975$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $345$ | $121095$ | $41785020$ | $14498098875$ | $5030917806975$ | $1745729163556560$ | $605767994916035205$ | $210201493923815749875$ | $72939918399246737305380$ | $25310151684669946678935975$ |
Jacobians and polarizations
This isogeny class is principally polarizable and contains the Jacobians of 16 curves (of which 0 are hyperelliptic):
- $y^2=x^3+344 x+341$
- $y^2=x^3+282 x+217$
- $y^2=x^3+246 x+246$
- $y^2=x^3+317 x+317$
- $y^2=x^3+121 x+121$
- $y^2=x^3+337 x+337$
- $y^2=x^3+188 x+29$
- $y^2=x^3+338 x+329$
- $y^2=x^3+308 x+308$
- $y^2=x^3+96 x+192$
- $y^2=x^3+161 x+322$
- $y^2=x^3+278 x+278$
- $y^2=x^3+319 x+291$
- $y^2=x^3+245 x+245$
- $y^2=x^3+6 x+6$
- $y^2=x^3+145 x+145$
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 \(\Q(\sqrt{-1379}) \). |
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.d | $2$ | (not in LMFDB) |