Invariants
| Base field: | $\F_{191}$ |
| Dimension: | $2$ |
| L-polynomial: | $( 1 - 27 x + 191 x^{2} )( 1 - 26 x + 191 x^{2} )$ |
| $1 - 53 x + 1084 x^{2} - 10123 x^{3} + 36481 x^{4}$ | |
| Frobenius angles: | $\pm0.0686610702072$, $\pm0.110219473395$ |
| Angle rank: | $2$ (numerical) |
| Jacobians: | $0$ |
This isogeny class is not simple, primitive, ordinary, and not supersingular. It is principally polarizable.
Newton polygon
This isogeny class is ordinary.
| $p$-rank: | $2$ |
| Slopes: | $[0, 0, 1, 1]$ |
Point counts
Point counts of the abelian variety
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $27390$ | $1307653380$ | $48503242850040$ | $1771116211426367520$ | $64614968004475421222250$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $139$ | $35841$ | $6960982$ | $1330802441$ | $254194586549$ | $48551229231498$ | $9273284351441459$ | $1771197288542903281$ | $338298681609668585002$ | $64615048178642180519001$ |
Jacobians and polarizations
This isogeny class is principally polarizable, but does not contain a Jacobian.
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{191}$.
Endomorphism algebra over $\F_{191}$| The isogeny class factors as 1.191.abb $\times$ 1.191.aba and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is: |
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.ab_ami | $2$ | (not in LMFDB) |
| 2.191.b_ami | $2$ | (not in LMFDB) |
| 2.191.cb_bps | $2$ | (not in LMFDB) |