Invariants
| Base field: | $\F_{283}$ |
| Dimension: | $1$ |
| L-polynomial: | $1 + 16 x + 283 x^{2}$ |
| Frobenius angles: | $\pm0.657751156156$ |
| Angle rank: | $1$ (numerical) |
| Number field: | \(\Q(\sqrt{-219}) \) |
| 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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $300$ | $80400$ | $22655700$ | $6414312000$ | $1815233821500$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $300$ | $80400$ | $22655700$ | $6414312000$ | $1815233821500$ | $513710657053200$ | $145380128839155300$ | $41142576400775328000$ | $11643349118741960474700$ | $3295067800663993822842000$ |
Jacobians and polarizations
This isogeny class is principally polarizable and contains the Jacobians of 16 curves (of which 0 are hyperelliptic):
- $y^2=x^3+145 x+7$
- $y^2=x^3+180 x+180$
- $y^2=x^3+68 x+68$
- $y^2=x^3+194 x+194$
- $y^2=x^3+238 x+193$
- $y^2=x^3+28 x+56$
- $y^2=x^3+198 x+113$
- $y^2=x^3+181 x+181$
- $y^2=x^3+98 x+196$
- $y^2=x^3+72 x+144$
- $y^2=x^3+167 x+167$
- $y^2=x^3+59 x+118$
- $y^2=x^3+204 x+204$
- $y^2=x^3+64 x+128$
- $y^2=x^3+45 x+45$
- $y^2=x^3+71 x+71$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{283}$.
Endomorphism algebra over $\F_{283}$| The endomorphism algebra of this simple isogeny class is \(\Q(\sqrt{-219}) \). |
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 |
|---|---|---|
| 1.283.aq | $2$ | (not in LMFDB) |