Invariants
Base field: | $\F_{283}$ |
Dimension: | $1$ |
L-polynomial: | $1 - 21 x + 283 x^{2}$ |
Frobenius angles: | $\pm0.285441245296$ |
Angle rank: | $1$ (numerical) |
Number field: | \(\Q(\sqrt{-691}) \) |
Galois group: | $C_2$ |
Jacobians: | $5$ |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $263$ | $80215$ | $22673756$ | $6414392475$ | $1815232772513$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $263$ | $80215$ | $22673756$ | $6414392475$ | $1815232772513$ | $513710673664720$ | $145380127831265051$ | $41142576383985748275$ | $11643349118997344953988$ | $3295067800666375783847575$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 5 curves (of which all are hyperelliptic), and hence is principally polarizable:
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{283}$.
Endomorphism algebra over $\F_{283}$The endomorphism algebra of this simple isogeny class is \(\Q(\sqrt{-691}) \). |
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 |
---|---|---|
1.283.v | $2$ | (not in LMFDB) |