Invariants
| Base field: | $\F_{163}$ |
| Dimension: | $2$ |
| L-polynomial: | $1 - 45 x + 824 x^{2} - 7335 x^{3} + 26569 x^{4}$ |
| Frobenius angles: | $\pm0.0358759288257$, $\pm0.220913488148$ |
| Angle rank: | $2$ (numerical) |
| Number field: | 4.0.2395800.1 |
| Galois group: | $D_{4}$ |
| Jacobians: | $8$ |
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: | $2$ |
| Slopes: | $[0, 0, 1, 1]$ |
Point counts
Point counts of the abelian variety
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $20014$ | $695966836$ | $18747185129896$ | $498312683291570976$ | $13239643863120727830514$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $119$ | $26193$ | $4328858$ | $705913561$ | $115063685669$ | $18755367337122$ | $3057125147239583$ | $498311412391264753$ | $81224760506321124254$ | $13239635966737146917553$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 8 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=8x^6+139x^5+82x^4+109x^3+142x^2+86x+37$
- $y^2=103x^6+30x^5+130x^4+124x^3+72x^2+79x+14$
- $y^2=115x^6+139x^5+147x^4+86x^3+105x^2+127x+95$
- $y^2=70x^6+154x^5+72x^4+60x^3+7x^2+111x+140$
- $y^2=67x^6+37x^5+3x^4+159x^3+6x^2+114x+96$
- $y^2=74x^6+125x^5+95x^4+34x^3+58x^2+27x+151$
- $y^2=144x^6+57x^5+8x^4+12x^3+106x^2+132x+16$
- $y^2=4x^6+135x^5+162x^4+27x^3+25x^2+76$
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 4.0.2395800.1. |
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 |
|---|---|---|
| 2.163.bt_bfs | $2$ | (not in LMFDB) |