Invariants
Base field: | $\F_{167}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 47 x + 883 x^{2} - 7849 x^{3} + 27889 x^{4}$ |
Frobenius angles: | $\pm0.0653585255984$, $\pm0.182853389423$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.925613.1 |
Galois group: | $D_{4}$ |
Jacobians: | $9$ |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $20877$ | $765538713$ | $21678615651267$ | $604966396090831389$ | $16871969707024828628112$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $121$ | $27447$ | $4654597$ | $777795395$ | $129892307276$ | $21691967385051$ | $3622557647310527$ | $604967117254049395$ | $101029508529127859407$ | $16871927924826638687262$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 9 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=53x^6+110x^5+92x^4+11x^3+90x^2+84x+139$
- $y^2=35x^6+166x^5+69x^4+31x^3+117x^2+157x+117$
- $y^2=101x^6+128x^5+159x^4+133x^3+6x^2+76x+97$
- $y^2=23x^6+94x^5+157x^4+9x^3+101x^2+155x+149$
- $y^2=10x^6+120x^5+160x^4+77x^3+123x^2+64x+143$
- $y^2=49x^6+104x^5+100x^4+27x^3+113x^2+148x+126$
- $y^2=74x^6+8x^5+13x^4+114x^3+141x^2+26x+161$
- $y^2=140x^6+37x^5+18x^4+165x^3+34x^2+22x+102$
- $y^2=8x^6+124x^5+153x^4+112x^3+65x^2+96x+9$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{167}$.
Endomorphism algebra over $\F_{167}$The endomorphism algebra of this simple isogeny class is 4.0.925613.1. |
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 |
---|---|---|
2.167.bv_bhz | $2$ | (not in LMFDB) |