Invariants
Base field: | $\F_{167}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 48 x + 907 x^{2} - 8016 x^{3} + 27889 x^{4}$ |
Frobenius angles: | $\pm0.0298610959797$, $\pm0.169479775008$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.145296.1 |
Galois group: | $D_{4}$ |
Jacobians: | $6$ |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $20733$ | $764239113$ | $21673191542004$ | $604949758123365369$ | $16871927482105786543893$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $120$ | $27400$ | $4653432$ | $777774004$ | $129891982200$ | $21691963020310$ | $3622557591581160$ | $604967116504131364$ | $101029508517559028904$ | $16871927924626240219000$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 6 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=69x^6+122x^5+32x^4+106x^3+39x^2+144x+149$
- $y^2=102x^6+107x^5+37x^4+38x^3+153x^2+5x+79$
- $y^2=79x^6+26x^5+119x^4+14x^3+4x^2+57x+6$
- $y^2=133x^6+152x^5+64x^4+136x^3+92x^2+111x+35$
- $y^2=126x^6+3x^5+88x^4+109x^3+21x^2+135x+143$
- $y^2=127x^6+161x^5+108x^4+118x^3+26x^2+77x+81$
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 4.0.145296.1. |
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.bw_bix | $2$ | (not in LMFDB) |