Invariants
Base field: | $\F_{181}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 51 x + 1011 x^{2} - 9231 x^{3} + 32761 x^{4}$ |
Frobenius angles: | $\pm0.0467121644153$, $\pm0.139008714891$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.50125.1 |
Galois group: | $D_{4}$ |
Jacobians: | $4$ |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $24491$ | $1054460005$ | $35128277447231$ | $1151890423380452005$ | $37738568154960421158416$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $131$ | $32183$ | $5924081$ | $1073240043$ | $194264097206$ | $35161831059383$ | $6364291003667441$ | $1151936659008828403$ | $208500535079258968451$ | $37738596847047153800198$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 4 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=17x^6+4x^5+101x^4+9x^3+130x^2+151x+166$
- $y^2=161x^6+25x^5+166x^4+14x^3+129x^2+151x+22$
- $y^2=135x^6+51x^5+156x^4+48x^3+40x^2+75x+64$
- $y^2=61x^6+88x^5+146x^4+56x^3+14x^2+152x+146$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{181}$.
Endomorphism algebra over $\F_{181}$The endomorphism algebra of this simple isogeny class is 4.0.50125.1. |
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 |
---|---|---|
2.181.bz_bmx | $2$ | (not in LMFDB) |