Invariants
Base field: | $\F_{167}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 47 x + 882 x^{2} - 7849 x^{3} + 27889 x^{4}$ |
Frobenius angles: | $\pm0.0472430896314$, $\pm0.188637795115$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.219929.1 |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $20876$ | $765481168$ | $21677957802800$ | $604962268662857024$ | $16871951056366484662996$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $121$ | $27445$ | $4654456$ | $777790089$ | $129892163691$ | $21691964264590$ | $3622557589898053$ | $604967116334678769$ | $101029508516127902632$ | $16871927924663214553725$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 12 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=91x^6+23x^5+124x^4+122x^3+86x^2+161x+28$
- $y^2=143x^6+8x^5+3x^4+139x^3+59x^2+82x+23$
- $y^2=50x^6+27x^5+162x^4+105x^3+121x^2+15x+112$
- $y^2=109x^6+108x^5+151x^4+96x^3+18x^2+116x+138$
- $y^2=152x^6+35x^5+11x^4+45x^3+27x^2+137x+105$
- $y^2=16x^6+49x^5+115x^4+37x^3+54x^2+32x+123$
- $y^2=70x^6+38x^5+44x^4+47x^3+111x^2+81x+102$
- $y^2=44x^6+165x^5+122x^4+33x^3+138x^2+7x+26$
- $y^2=112x^6+40x^5+146x^4+126x^3+104x^2+104x+161$
- $y^2=51x^6+159x^5+58x^4+120x^3+97x^2+139x+41$
- $y^2=70x^6+53x^5+8x^4+75x^3+26x^2+135x+70$
- $y^2=78x^6+161x^5+69x^4+96x^3+62x^2+61x+115$
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 4.0.219929.1. |
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_bhy | $2$ | (not in LMFDB) |