Invariants
| Base field: | $\F_{163}$ |
| Dimension: | $2$ |
| L-polynomial: | $1 - 47 x + 877 x^{2} - 7661 x^{3} + 26569 x^{4}$ |
| Frobenius angles: | $\pm0.0855301227133$, $\pm0.159842173573$ |
| Angle rank: | $2$ (numerical) |
| Number field: | 4.0.173525.1 |
| 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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $19739$ | $693924545$ | $18741741484901$ | $498309467549648525$ | $13239681415912501372944$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $117$ | $26115$ | $4327599$ | $705909003$ | $115064012032$ | $18755378526495$ | $3057125377918869$ | $498311415994666563$ | $81224760550822403187$ | $13239635967154889210950$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 8 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=112x^6+148x^5+46x^3+10x^2+84x+24$
- $y^2=75x^6+102x^5+139x^4+110x^3+135x^2+120x+35$
- $y^2=129x^6+23x^5+54x^4+40x^3+38x^2+143x+156$
- $y^2=132x^6+59x^5+120x^4+53x^3+23x^2+43x+142$
- $y^2=2x^6+32x^5+28x^4+95x^3+129x^2+104x+75$
- $y^2=67x^6+127x^5+89x^4+138x^3+78x^2+79x+112$
- $y^2=21x^6+62x^5+97x^4+162x^3+x^2+161x+51$
- $y^2=11x^6+134x^5+2x^4+124x^3+162x^2+68x+58$
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 4.0.173525.1. |
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.bv_bht | $2$ | (not in LMFDB) |