Invariants
Base field: | $\F_{163}$ |
Dimension: | $1$ |
L-polynomial: | $1 - 13 x + 163 x^{2}$ |
Frobenius angles: | $\pm0.329971199733$ |
Angle rank: | $1$ (numerical) |
Number field: | \(\Q(\sqrt{-483}) \) |
Galois group: | $C_2$ |
Jacobians: | $4$ |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $151$ | $26727$ | $4334908$ | $705940251$ | $115063309321$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $151$ | $26727$ | $4334908$ | $705940251$ | $115063309321$ | $18755360933904$ | $3057125179000939$ | $498311414918321523$ | $81224760551797316164$ | $13239635967153593853207$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 4 curves (of which all are hyperelliptic), and hence is principally polarizable:
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{163}$.
Endomorphism algebra over $\F_{163}$The endomorphism algebra of this simple isogeny class is \(\Q(\sqrt{-483}) \). |
Base change
This is a primitive isogeny class.
Twists
Below is a list of all twists of this isogeny class.
Twist | Extension degree | Common base change |
---|---|---|
1.163.n | $2$ | (not in LMFDB) |