Invariants
| Base field: | $\F_{463}$ |
| Dimension: | $1$ |
| L-polynomial: | $1 - 22 x + 463 x^{2}$ |
| Frobenius angles: | $\pm0.329196197449$ |
| Angle rank: | $1$ (numerical) |
| Number field: | \(\Q(\sqrt{-38}) \) |
| 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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $442$ | $214812$ | $99272758$ | $45954301536$ | $21276729474442$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $442$ | $214812$ | $99272758$ | $45954301536$ | $21276729474442$ | $9851127439703004$ | $4561072093748390662$ | $2111776380583278634368$ | $977752464194685218569114$ | $452699390921255745586253532$ |
Jacobians and polarizations
This isogeny class is principally polarizable and contains the Jacobians of 18 curves (of which 0 are hyperelliptic):
- $y^2=x^3+227 x+218$
- $y^2=x^3+402 x+402$
- $y^2=x^3+209 x+209$
- $y^2=x^3+32 x+96$
- $y^2=x^3+348 x+348$
- $y^2=x^3+306 x+455$
- $y^2=x^3+27 x+27$
- $y^2=x^3+247 x+247$
- $y^2=x^3+399 x+271$
- $y^2=x^3+164 x+29$
- $y^2=x^3+355 x+355$
- $y^2=x^3+338 x+338$
- $y^2=x^3+426 x+352$
- $y^2=x^3+447 x+447$
- $y^2=x^3+114 x+342$
- $y^2=x^3+193 x+116$
- $y^2=x^3+414 x+316$
- $y^2=x^3+199 x+134$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{463}$.
Endomorphism algebra over $\F_{463}$| The endomorphism algebra of this simple isogeny class is \(\Q(\sqrt{-38}) \). |
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 |
|---|---|---|
| 1.463.w | $2$ | (not in LMFDB) |