Invariants
Base field: | $\F_{163}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 46 x + 850 x^{2} - 7498 x^{3} + 26569 x^{4}$ |
Frobenius angles: | $\pm0.0486964346780$, $\pm0.197735354640$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.83600.1 |
Galois group: | $D_{4}$ |
Jacobians: | $12$ |
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: | $2$ |
Slopes: | $[0, 0, 1, 1]$ |
Point counts
Point counts of the abelian variety
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $19876$ | $694944464$ | $18744416964244$ | $498310417152102656$ | $13239657662621701104916$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $118$ | $26154$ | $4328218$ | $705910350$ | $115063805598$ | $18755371534458$ | $3057125227573570$ | $498311413478906334$ | $81224760516505231654$ | $13239635966779193306314$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 12 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=81x^6+57x^5+65x^4+123x^3+130x^2+47x+73$
- $y^2=121x^6+15x^5+159x^3+74x^2+63x+137$
- $y^2=45x^6+30x^5+88x^4+48x^3+113x^2+25x+126$
- $y^2=28x^6+51x^5+139x^4+123x^3+161x^2+63x+116$
- $y^2=55x^6+26x^5+154x^4+103x^3+119x^2+24x+94$
- $y^2=92x^6+28x^5+41x^4+132x^3+139x^2+77x+59$
- $y^2=55x^6+72x^5+87x^4+134x^3+40x^2+74x+46$
- $y^2=153x^6+91x^5+117x^4+54x^3+145x^2+87x+160$
- $y^2=139x^6+110x^5+77x^4+92x^3+74x^2+14x+103$
- $y^2=71x^6+42x^5+136x^4+29x^3+30x^2+130x+138$
- $y^2=144x^6+84x^5+125x^4+95x^3+42x^2+162x+8$
- $y^2=11x^6+155x^5+75x^4+45x^3+82x^2+58x+29$
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 4.0.83600.1. |
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.bu_bgs | $2$ | (not in LMFDB) |