Invariants
Base field: | $\F_{211}$ |
Dimension: | $2$ |
L-polynomial: | $( 1 - 29 x + 211 x^{2} )( 1 - 27 x + 211 x^{2} )$ |
$1 - 56 x + 1205 x^{2} - 11816 x^{3} + 44521 x^{4}$ | |
Frobenius angles: | $\pm0.0189887838440$, $\pm0.120343810545$ |
Angle rank: | $2$ (numerical) |
Jacobians: | $2$ |
This isogeny class is not 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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $33855$ | $1950014145$ | $88164960786000$ | $3928615670916958905$ | $174913645417201845981375$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $156$ | $43796$ | $9385308$ | $1982027716$ | $418226372076$ | $88245934104998$ | $18619893253193556$ | $3928797478805980036$ | $828976267946473232868$ | $174913992535387353817076$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 2 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=63x^6+42x^5+155x^4+106x^3+129x^2+26x+140$
- $y^2=91x^6+186x^5+180x^4+116x^3+5x^2+175x+164$
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.abb 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.