Invariants
Base field: | $\F_{211}$ |
Dimension: | $2$ |
L-polynomial: | $( 1 - 29 x + 211 x^{2} )( 1 - 28 x + 211 x^{2} )$ |
$1 - 57 x + 1234 x^{2} - 12027 x^{3} + 44521 x^{4}$ | |
Frobenius angles: | $\pm0.0189887838440$, $\pm0.0859092328146$ |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $33672$ | $1947588480$ | $88149602181600$ | $3928542742015557120$ | $174913356727946239692312$ |
Point counts of the (virtual) curve
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $155$ | $43741$ | $9383672$ | $1981990921$ | $418225681805$ | $88245922947478$ | $18619893098499575$ | $3928797477068924881$ | $828976267934413244552$ | $174913992535471825730701$ |
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 $\F_{211}$.
Endomorphism algebra over $\F_{211}$The isogeny class factors as 1.211.abd $\times$ 1.211.abc 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.