Invariants
Base field: | $\F_{73}$ |
Dimension: | $1$ |
L-polynomial: | $1 - 10 x + 73 x^{2}$ |
Frobenius angles: | $\pm0.301013746420$ |
Angle rank: | $1$ (numerical) |
Number field: | \(\Q(\sqrt{-3}) \) |
Galois group: | $C_2$ |
Jacobians: | $8$ |
Isomorphism classes: | 8 |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $64$ | $5376$ | $390208$ | $28406784$ | $2073070144$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $64$ | $5376$ | $390208$ | $28406784$ | $2073070144$ | $151333588224$ | $11047392244288$ | $806460075724800$ | $58871587004636224$ | $4297625833847598336$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 8 curves (of which all are hyperelliptic), and hence is principally polarizable:
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{73}$.
Endomorphism algebra over $\F_{73}$The endomorphism algebra of this simple isogeny class is \(\Q(\sqrt{-3}) \). |
Base change
This is a primitive isogeny class.