Invariants
Base field: | $\F_{191}$ |
Dimension: | $2$ |
L-polynomial: | $( 1 - 25 x + 191 x^{2} )( 1 - 24 x + 191 x^{2} )$ |
$1 - 49 x + 982 x^{2} - 9359 x^{3} + 36481 x^{4}$ | |
Frobenius angles: | $\pm0.140267993779$, $\pm0.165219579186$ |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $28056$ | $1315040832$ | $48541680381600$ | $1771262819186515200$ | $64615418719063270735656$ |
Point counts of the (virtual) curve
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $143$ | $36045$ | $6966500$ | $1330912601$ | $254196359653$ | $48551252448942$ | $9273284580130483$ | $1771197289534171921$ | $338298681586055701100$ | $64615048177797604994805$ |
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.az $\times$ 1.191.ay 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_aik | $2$ | (not in LMFDB) |
2.191.b_aik | $2$ | (not in LMFDB) |
2.191.bx_blu | $2$ | (not in LMFDB) |