Invariants
Base field: | $\F_{11}$ |
Dimension: | $3$ |
L-polynomial: | $( 1 - 6 x + 11 x^{2} )( 1 - 9 x + 41 x^{2} - 99 x^{3} + 121 x^{4} )$ |
$1 - 15 x + 106 x^{2} - 444 x^{3} + 1166 x^{4} - 1815 x^{5} + 1331 x^{6}$ | |
Frobenius angles: | $\pm0.140218899004$, $\pm0.178435994483$, $\pm0.329700688269$ |
Angle rank: | $3$ (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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $330$ | $1609740$ | $2473874370$ | $3209654147040$ | $4199877907500000$ |
Point counts of the (virtual) curve
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $-3$ | $109$ | $1395$ | $14969$ | $161922$ | $1773841$ | $19497237$ | $214404929$ | $2358078615$ | $25937462824$ |
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.ag $\times$ 2.11.aj_bp 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.