Invariants
| Base field: | $\F_{223}$ |
| Dimension: | $1$ |
| L-polynomial: | $1 - 16 x + 223 x^{2}$ |
| Frobenius angles: | $\pm0.320040401556$ |
| Angle rank: | $1$ (numerical) |
| Number field: | \(\Q(\sqrt{-159}) \) |
| Galois group: | $C_2$ |
| Jacobians: | $20$ |
| Isomorphism classes: | 20 |
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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $208$ | $49920$ | $11096176$ | $2473036800$ | $551472617488$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $208$ | $49920$ | $11096176$ | $2473036800$ | $551472617488$ | $122978474760960$ | $27424204421953456$ | $6115597640823091200$ | $1363778273764480978768$ | $304122555035049938553600$ |
Jacobians and polarizations
This isogeny class is principally polarizable and contains the Jacobians of 20 curves (of which 0 are hyperelliptic):
- $y^2=x^3+112 x+113$
- $y^2=x^3+125 x+125$
- $y^2=x^3+179 x+91$
- $y^2=x^3+194 x+194$
- $y^2=x^3+51 x+51$
- $y^2=x^3+222 x+222$
- $y^2=x^3+28 x+28$
- $y^2=x^3+54 x+54$
- $y^2=x^3+79 x+79$
- $y^2=x^3+220 x+214$
- $y^2=x^3+113 x+113$
- $y^2=x^3+37 x+37$
- $y^2=x^3+140 x+140$
- $y^2=x^3+104 x+104$
- $y^2=x^3+200 x+200$
- $y^2=x^3+178 x+178$
- $y^2=x^3+87 x+38$
- $y^2=x^3+182 x+100$
- $y^2=x^3+174 x+76$
- $y^2=x^3+121 x+140$
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 \(\Q(\sqrt{-159}) \). |
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.q | $2$ | (not in LMFDB) |