Invariants
Base field: | $\F_{431}$ |
Dimension: | $1$ |
L-polynomial: | $1 - 12 x + 431 x^{2}$ |
Frobenius angles: | $\pm0.406673970505$ |
Angle rank: | $1$ (numerical) |
Number field: | \(\Q(\sqrt{-395}) \) |
Galois group: | $C_2$ |
Jacobians: | $32$ |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $420$ | $186480$ | $80076780$ | $34507005120$ | $14872573600500$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $420$ | $186480$ | $80076780$ | $34507005120$ | $14872573600500$ | $6410082497883120$ | $2762745572456536380$ | $1190743340507208794880$ | $513210379737108788868420$ | $221193673666962401245302000$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 32 curves (of which all are hyperelliptic), and hence is principally polarizable:
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{431}$.
Endomorphism algebra over $\F_{431}$The endomorphism algebra of this simple isogeny class is \(\Q(\sqrt{-395}) \). |
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 |
---|---|---|
1.431.m | $2$ | (not in LMFDB) |