Invariants
| Base field: | $\F_{191}$ |
| Dimension: | $2$ |
| L-polynomial: | $1 - 48 x + 945 x^{2} - 9168 x^{3} + 36481 x^{4}$ |
| Frobenius angles: | $\pm0.0160200271430$, $\pm0.235843406874$ |
| Angle rank: | $2$ (numerical) |
| Number field: | 4.0.113737.1 |
| 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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $28211$ | $1315845673$ | $48537176259584$ | $1771197711718318537$ | $64615016685856127984531$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $144$ | $36068$ | $6965856$ | $1330863684$ | $254194778064$ | $48551216642174$ | $9273283949383920$ | $1771197280708311940$ | $338298681492405868320$ | $64615048177214430184868$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 6 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=132x^6+77x^5+93x^4+50x^3+170x^2+180x+173$
- $y^2=161x^6+123x^5+183x^4+155x^3+34x^2+21x+52$
- $y^2=97x^6+13x^5+162x^4+154x^3+173x^2+24x+142$
- $y^2=91x^6+141x^5+183x^4+128x^3+59x^2+71x+62$
- $y^2=121x^6+5x^5+145x^4+29x^3+130x^2+190x+53$
- $y^2=71x^6+36x^5+147x^4+113x^3+142x^2+71x+164$
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 4.0.113737.1. |
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.bw_bkj | $2$ | (not in LMFDB) |