Invariants
Base field: | $\F_{277}$ |
Dimension: | $1$ |
L-polynomial: | $1 + 5 x + 277 x^{2}$ |
Frobenius angles: | $\pm0.547995123194$ |
Angle rank: | $1$ (numerical) |
Number field: | \(\Q(\sqrt{-3}) \) |
Galois group: | $C_2$ |
Jacobians: | $7$ |
This isogeny class is simple and geometrically simple, primitive, ordinary, and not supersingular. It is principally polarizable and contains a Jacobian.
Newton polygon
This isogeny class is ordinary.
$p$-rank: | $1$ |
Slopes: | $[0, 1]$ |
Point counts
Point counts of the abelian variety
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $283$ | $77259$ | $21249904$ | $5887213059$ | $1630794773383$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $283$ | $77259$ | $21249904$ | $5887213059$ | $1630794773383$ | $451729694235456$ | $125129117411678299$ | $34660765689356208675$ | $9601032097306020540208$ | $2659485890900924930274339$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 7 curves (of which all are hyperelliptic), and hence is principally polarizable:
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{277}$.
Endomorphism algebra over $\F_{277}$The endomorphism algebra of this simple isogeny class is \(\Q(\sqrt{-3}) \). |
Base change
This is a primitive isogeny class.