Invariants
| Base field: | $\F_{383}$ |
| Dimension: | $1$ |
| L-polynomial: | $1 - 20 x + 383 x^{2}$ |
| Frobenius angles: | $\pm0.329284048955$ |
| 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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $364$ | $147056$ | $56196868$ | $21517822144$ | $8241262273244$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $364$ | $147056$ | $56196868$ | $21517822144$ | $8241262273244$ | $3156404314844144$ | $1208902894230830708$ | $463009808992333075200$ | $177332756838151830421324$ | $67918445868701679061546736$ |
Jacobians and polarizations
This isogeny class is principally polarizable and contains the Jacobians of 12 curves (of which 0 are hyperelliptic):
- $y^2=x^3+28 x+140$
- $y^2=x^3+61 x+61$
- $y^2=x^3+190 x+190$
- $y^2=x^3+366 x+298$
- $y^2=x^3+30 x+30$
- $y^2=x^3+156 x+156$
- $y^2=x^3+57 x+285$
- $y^2=x^3+50 x+250$
- $y^2=x^3+89 x+62$
- $y^2=x^3+275 x+275$
- $y^2=x^3+255 x+255$
- $y^2=x^3+258 x+258$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{383}$.
Endomorphism algebra over $\F_{383}$| 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 |
|---|---|---|
| 1.383.u | $2$ | (not in LMFDB) |