Invariants
| Base field: | $\F_{83}$ |
| Dimension: | $1$ |
| L-polynomial: | $1 - 12 x + 83 x^{2}$ |
| Frobenius angles: | $\pm0.271155063531$ |
| Angle rank: | $1$ (numerical) |
| Number field: | \(\Q(\sqrt{-47}) \) |
| Galois group: | $C_2$ |
| Jacobians: | $10$ |
| Isomorphism classes: | 10 |
| Cyclic group of points: | no |
| Non-cyclic primes: | $2$ |
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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $72$ | $6912$ | $573048$ | $47471616$ | $3939095592$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $72$ | $6912$ | $573048$ | $47471616$ | $3939095592$ | $326939929344$ | $27136041100632$ | $2252292150325248$ | $186940255106561544$ | $15516041192064652032$ |
Jacobians and polarizations
This isogeny class is principally polarizable and contains the Jacobians of 10 curves (of which 0 are hyperelliptic):
- $y^2=x^3+70 x+70$
- $y^2=x^3+57 x+57$
- $y^2=x^3+28 x+28$
- $y^2=x^3+53 x+53$
- $y^2=x^3+14 x+28$
- $y^2=x^3+60 x+60$
- $y^2=x^3+77 x+77$
- $y^2=x^3+31 x+31$
- $y^2=x^3+50 x+17$
- $y^2=x^3+37 x+74$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{83}$.
Endomorphism algebra over $\F_{83}$| The endomorphism algebra of this simple isogeny class is \(\Q(\sqrt{-47}) \). |
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 |
|---|---|---|
| 1.83.m | $2$ | (not in LMFDB) |