Invariants
Base field: | $\F_{173}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 45 x + 845 x^{2} - 7785 x^{3} + 29929 x^{4}$ |
Frobenius angles: | $\pm0.0929373847626$, $\pm0.228622914131$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.14449221.1 |
Galois group: | $D_{4}$ |
Jacobians: | $40$ |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $22945$ | $885791725$ | $26806659400885$ | $802389850119073125$ | $24013904224903563739600$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $129$ | $29595$ | $5177313$ | $895779283$ | $154964513994$ | $26808759257235$ | $4637914346264853$ | $802359178177642243$ | $138808137873705675309$ | $24013807852720433431350$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 40 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=88x^6+99x^5+101x^4+132x^3+166x^2+137x+110$
- $y^2=45x^6+136x^5+163x^4+170x^3+76x^2+33x+147$
- $y^2=147x^6+68x^5+82x^4+66x^3+84x^2+36x+107$
- $y^2=158x^6+14x^5+76x^4+147x^3+152x^2+128x+5$
- $y^2=111x^6+65x^5+38x^4+110x^3+14x^2+82x+79$
- $y^2=14x^6+15x^5+73x^4+158x^3+166x^2+131x+7$
- $y^2=160x^6+43x^5+118x^4+89x^3+6x^2+169x+82$
- $y^2=79x^6+70x^5+69x^4+113x^3+133x^2+131x+40$
- $y^2=6x^6+26x^5+67x^4+65x^3+9x^2+75x+149$
- $y^2=77x^6+67x^5+28x^4+155x^3+100x^2+162x+41$
- $y^2=66x^6+59x^5+27x^4+84x^3+147x^2+144x+153$
- $y^2=165x^6+79x^5+38x^4+90x^3+167x^2+5x+85$
- $y^2=136x^6+117x^5+94x^4+78x^3+140x^2+98x+58$
- $y^2=68x^6+155x^5+75x^4+80x^3+33x^2+68x+108$
- $y^2=149x^6+124x^5+51x^4+10x^3+154x^2+105x+51$
- $y^2=57x^6+36x^5+42x^4+163x^3+136x^2+68x+66$
- $y^2=19x^6+81x^5+167x^4+75x^3+135x^2+94x+56$
- $y^2=42x^6+26x^5+159x^4+158x^3+128x^2+64x+151$
- $y^2=27x^6+143x^5+119x^4+6x^3+69x^2+9x+102$
- $y^2=79x^6+32x^5+132x^4+83x^3+160x^2+38x+98$
- and 20 more
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 4.0.14449221.1. |
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 |
---|---|---|
2.173.bt_bgn | $2$ | (not in LMFDB) |