Invariants
Base field: | $\F_{191}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 53 x + 1083 x^{2} - 10123 x^{3} + 36481 x^{4}$ |
Frobenius angles: | $\pm0.0128489088744$, $\pm0.129572401751$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.3725.1 |
Galois group: | $D_{4}$ |
Jacobians: | $1$ |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $27389$ | $1307578249$ | $48502133155475$ | $1771107024866409149$ | $64614911891852335078384$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $139$ | $35839$ | $6960823$ | $1330795539$ | $254194365804$ | $48551223409363$ | $9273284217551269$ | $1771197285772244499$ | $338298681557075638093$ | $64615048177715295394254$ |
Jacobians and polarizations
This isogeny class contains the Jacobian of 1 curve (which is hyperelliptic), and hence is principally polarizable:
- $y^2=147x^6+151x^5+175x^4+102x^3+164x^2+62x+185$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{191}$.
Endomorphism algebra over $\F_{191}$The endomorphism algebra of this simple isogeny class is 4.0.3725.1. |
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 |
---|---|---|
2.191.cb_bpr | $2$ | (not in LMFDB) |