Invariants
Base field: | $\F_{463}$ |
Dimension: | $1$ |
L-polynomial: | $1 - 8 x + 463 x^{2}$ |
Frobenius angles: | $\pm0.440481322678$ |
Angle rank: | $1$ (numerical) |
Number field: | \(\Q(\sqrt{-447}) \) |
Galois group: | $C_2$ |
Jacobians: | $28$ |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $456$ | $215232$ | $99263448$ | $45953753856$ | $21276726136296$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $456$ | $215232$ | $99263448$ | $45953753856$ | $21276726136296$ | $9851127723751104$ | $4561072100336970744$ | $2111776380538953796608$ | $977752464190755881314824$ | $452699390921217335710026432$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 28 curves (of which all are hyperelliptic), and hence is principally polarizable:
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{463}$.
Endomorphism algebra over $\F_{463}$The endomorphism algebra of this simple isogeny class is \(\Q(\sqrt{-447}) \). |
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 |
---|---|---|
1.463.i | $2$ | (not in LMFDB) |