Invariants
| Base field: | $\F_{163}$ |
| Dimension: | $1$ |
| L-polynomial: | $1 - 16 x + 163 x^{2}$ |
| Frobenius angles: | $\pm0.284442586616$ |
| Angle rank: | $1$ (numerical) |
| Number field: | \(\Q(\sqrt{-11}) \) |
| Galois group: | $C_2$ |
| Jacobians: | $12$ |
| Isomorphism classes: | 12 |
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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $148$ | $26640$ | $4334476$ | $705960000$ | $115063781188$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $148$ | $26640$ | $4334476$ | $705960000$ | $115063781188$ | $18755364341520$ | $3057125130676156$ | $498311413403040000$ | $81224760537230352628$ | $13239635967221344045200$ |
Jacobians and polarizations
This isogeny class is principally polarizable and contains the Jacobians of 12 curves (of which 0 are hyperelliptic):
- $y^2=x^3+155 x+155$
- $y^2=x^3+7 x+7$
- $y^2=x^3+143 x+123$
- $y^2=x^3+16 x+32$
- $y^2=x^3+44 x+44$
- $y^2=x^3+43 x+86$
- $y^2=x^3+128 x+93$
- $y^2=x^3+153 x+153$
- $y^2=x^3+103 x+103$
- $y^2=x^3+140 x+140$
- $y^2=x^3+21 x+21$
- $y^2=x^3+74 x+74$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{163}$.
Endomorphism algebra over $\F_{163}$| The endomorphism algebra of this simple isogeny class is \(\Q(\sqrt{-11}) \). |
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 |
|---|---|---|
| 1.163.q | $2$ | (not in LMFDB) |