Invariants
Base field: | $\F_{173}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 47 x + 895 x^{2} - 8131 x^{3} + 29929 x^{4}$ |
Frobenius angles: | $\pm0.0881869395452$, $\pm0.191285016768$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.1935557.1 |
Galois group: | $D_{4}$ |
Jacobians: | $18$ |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $22647$ | $883300941$ | $26798296309443$ | $802374923595026421$ | $24013906206530330034192$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $127$ | $29511$ | $5175697$ | $895762619$ | $154964526782$ | $26808763538511$ | $4637914441512521$ | $802359179383803763$ | $138808137880039455535$ | $24013807852601392577046$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 18 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=167x^6+92x^5+103x^4+104x^3+106x^2+12x+143$
- $y^2=3x^6+136x^5+11x^4+10x^3+23x^2+138x+148$
- $y^2=15x^6+6x^5+58x^4+97x^3+162x^2+51x+150$
- $y^2=120x^6+85x^5+170x^4+147x^3+163x^2+26x+77$
- $y^2=18x^6+120x^5+101x^4+145x^3+80x^2+143x+44$
- $y^2=72x^6+121x^5+26x^4+102x^3+14x^2+169x+40$
- $y^2=108x^6+17x^5+23x^4+60x^3+86x^2+29x+163$
- $y^2=103x^6+136x^5+37x^4+31x^3+32x^2+51x+2$
- $y^2=44x^6+138x^5+10x^4+112x^3+67x^2+164x+3$
- $y^2=42x^6+145x^5+128x^4+59x^3+14x^2+85x+51$
- $y^2=165x^6+13x^5+169x^4+5x^3+14x^2+3x+130$
- $y^2=120x^6+108x^5+50x^4+60x^3+151x^2+94x+127$
- $y^2=59x^6+117x^5+172x^4+105x^3+27x^2+117x+35$
- $y^2=36x^6+165x^5+114x^4+27x^3+49x^2+161x+36$
- $y^2=161x^6+14x^5+16x^4+124x^3+155x^2+93x+79$
- $y^2=89x^6+156x^5+3x^4+54x^3+10x^2+102x+88$
- $y^2=58x^6+112x^5+32x^4+163x^3+109x^2+71x+105$
- $y^2=10x^6+69x^5+90x^4+130x^3+145x^2+127x+86$
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 4.0.1935557.1. |
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.bv_bil | $2$ | (not in LMFDB) |