Invariants
| Base field: | $\F_{379}$ |
| Dimension: | $1$ |
| L-polynomial: | $1 - 28 x + 379 x^{2}$ |
| Frobenius angles: | $\pm0.244539788418$ |
| Angle rank: | $1$ (numerical) |
| Number field: | \(\Q(\sqrt{-183}) \) |
| 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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $352$ | $143616$ | $54449824$ | $20633023488$ | $7819811556832$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $352$ | $143616$ | $54449824$ | $20633023488$ | $7819811556832$ | $2963706969510144$ | $1123244935896194848$ | $425709831159700082688$ | $161344026024370262540896$ | $61149385863479498569349376$ |
Jacobians and polarizations
This isogeny class is principally polarizable and contains the Jacobians of 16 curves (of which 0 are hyperelliptic):
- $y^2=x^3+260 x+141$
- $y^2=x^3+159 x+318$
- $y^2=x^3+221 x+221$
- $y^2=x^3+66 x+132$
- $y^2=x^3+188 x+188$
- $y^2=x^3+150 x+300$
- $y^2=x^3+75 x+75$
- $y^2=x^3+107 x+107$
- $y^2=x^3+291 x+291$
- $y^2=x^3+250 x+250$
- $y^2=x^3+23 x+23$
- $y^2=x^3+131 x+262$
- $y^2=x^3+339 x+339$
- $y^2=x^3+161 x+322$
- $y^2=x^3+303 x+227$
- $y^2=x^3+329 x+279$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{379}$.
Endomorphism algebra over $\F_{379}$| The endomorphism algebra of this simple isogeny class is \(\Q(\sqrt{-183}) \). |
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 |
|---|---|---|
| 1.379.bc | $2$ | (not in LMFDB) |