Invariants
Base field: | $\F_{173}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 46 x + 873 x^{2} - 7958 x^{3} + 29929 x^{4}$ |
Frobenius angles: | $\pm0.121450667765$, $\pm0.193656994607$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.1388096.7 |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $22799$ | $884760793$ | $26804950732700$ | $802397519825511449$ | $24013969588009182886279$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $128$ | $29560$ | $5176982$ | $895787844$ | $154964935788$ | $26808769192510$ | $4637914507531916$ | $802359179984344644$ | $138808137882640709486$ | $24013807852549330375800$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 12 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=79x^6+20x^5+30x^4+121x^3+87x^2+100x+48$
- $y^2=168x^6+94x^5+49x^4+39x^3+85x^2+151x+6$
- $y^2=86x^6+106x^5+104x^4+57x^3+123x^2+163x+165$
- $y^2=137x^6+130x^5+84x^4+41x^3+65x^2+51x+152$
- $y^2=155x^6+92x^5+156x^4+20x^3+26x^2+102x+25$
- $y^2=82x^6+130x^5+13x^4+142x^3+80x^2+112x+35$
- $y^2=88x^6+19x^5+84x^4+111x^3+5x^2+148x+122$
- $y^2=105x^6+118x^5+96x^4+22x^3+171x^2+15x+5$
- $y^2=166x^6+118x^5+115x^4+20x^3+97x^2+148x+87$
- $y^2=15x^6+99x^5+107x^4+36x^3+32x^2+18x+125$
- $y^2=108x^6+29x^5+101x^4+131x^3+59x^2+119x+63$
- $y^2=143x^6+114x^5+4x^4+143x^3+98x^2+69x+74$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{173}$.
Endomorphism algebra over $\F_{173}$The endomorphism algebra of this simple isogeny class is 4.0.1388096.7. |
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 |
---|---|---|
2.173.bu_bhp | $2$ | (not in LMFDB) |