Invariants
Base field: | $\F_{191}$ |
Dimension: | $2$ |
L-polynomial: | $( 1 - 26 x + 191 x^{2} )( 1 - 25 x + 191 x^{2} )$ |
$1 - 51 x + 1032 x^{2} - 9741 x^{3} + 36481 x^{4}$ | |
Frobenius angles: | $\pm0.110219473395$, $\pm0.140267993779$ |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $27722$ | $1311416932$ | $48523525494968$ | $1771197872375495200$ | $64615240680028026608702$ |
Point counts of the (virtual) curve
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $141$ | $35945$ | $6963894$ | $1330863801$ | $254195659251$ | $48551245282442$ | $9273284555439381$ | $1771197290600549521$ | $338298681621325120074$ | $64615048178513941140305$ |
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.aba $\times$ 1.191.az 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_aki | $2$ | (not in LMFDB) |
2.191.b_aki | $2$ | (not in LMFDB) |
2.191.bz_bns | $2$ | (not in LMFDB) |