Invariants
Base field: | $\F_{11}$ |
Dimension: | $3$ |
L-polynomial: | $( 1 - 4 x + 11 x^{2} )( 1 - 5 x + 11 x^{2} )^{2}$ |
$1 - 14 x + 98 x^{2} - 408 x^{3} + 1078 x^{4} - 1694 x^{5} + 1331 x^{6}$ | |
Frobenius angles: | $\pm0.228229222880$, $\pm0.228229222880$, $\pm0.293962833700$ |
Angle rank: | $2$ (numerical) |
This isogeny class is not simple, primitive, ordinary, and not supersingular. It is principally polarizable.
Newton polygon
This isogeny class is ordinary.
$p$-rank: | $3$ |
Slopes: | $[0, 0, 0, 1, 1, 1]$ |
Point counts
Point counts of the abelian variety
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $392$ | $1812608$ | $2635337600$ | $3285352000000$ | $4217009424478312$ |
Point counts of the (virtual) curve
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $-2$ | $122$ | $1480$ | $15314$ | $162578$ | $1771724$ | $19473158$ | $214295714$ | $2357799160$ | $25937333882$ |
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 $\F_{11}$.
Endomorphism algebra over $\F_{11}$The isogeny class factors as 1.11.af 2 $\times$ 1.11.ae 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.