Invariants
| Base field: | $\F_{223}$ |
| Dimension: | $1$ |
| L-polynomial: | $1 + 8 x + 223 x^{2}$ |
| Frobenius angles: | $\pm0.586316404463$ |
| Angle rank: | $1$ (numerical) |
| Number field: | \(\Q(\sqrt{-23}) \) |
| Galois group: | $C_2$ |
| Jacobians: | $18$ |
| Isomorphism classes: | 18 |
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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $232$ | $50112$ | $11084728$ | $2472926976$ | $551474528392$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $232$ | $50112$ | $11084728$ | $2472926976$ | $551474528392$ | $122978495001024$ | $27424204349578072$ | $6115597642678238208$ | $1363778273743418456104$ | $304122555033155865796032$ |
Jacobians and polarizations
This isogeny class is principally polarizable and contains the Jacobians of 18 curves (of which 0 are hyperelliptic):
- $y^2=x^3+149 x+149$
- $y^2=x^3+12 x+12$
- $y^2=x^3+36 x+36$
- $y^2=x^3+104 x+89$
- $y^2=x^3+176 x+82$
- $y^2=x^3+195 x+139$
- $y^2=x^3+83 x+26$
- $y^2=x^3+191 x+191$
- $y^2=x^3+164 x+46$
- $y^2=x^3+13 x+13$
- $y^2=x^3+64 x+64$
- $y^2=x^3+181 x+97$
- $y^2=x^3+158 x+158$
- $y^2=x^3+48 x+144$
- $y^2=x^3+73 x+73$
- $y^2=x^3+100 x+100$
- $y^2=x^3+113 x+116$
- $y^2=x^3+208 x+208$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{223}$.
Endomorphism algebra over $\F_{223}$| The endomorphism algebra of this simple isogeny class is \(\Q(\sqrt{-23}) \). |
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 |
|---|---|---|
| 1.223.ai | $2$ | (not in LMFDB) |