Invariants
Base field: | $\F_{241}$ |
Dimension: | $1$ |
L-polynomial: | $1 - 20 x + 241 x^{2}$ |
Frobenius angles: | $\pm0.277208490946$ |
Angle rank: | $1$ (numerical) |
Number field: | \(\Q(\sqrt{-141}) \) |
Galois group: | $C_2$ |
Jacobians: | $8$ |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $222$ | $58164$ | $14003982$ | $3373512000$ | $812990649102$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $222$ | $58164$ | $14003982$ | $3373512000$ | $812990649102$ | $195930580408884$ | $47219272762032222$ | $11379844833331488000$ | $2742542606091601630782$ | $660952768069708958298804$ |
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 $\F_{241}$.
Endomorphism algebra over $\F_{241}$The endomorphism algebra of this simple isogeny class is \(\Q(\sqrt{-141}) \). |
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 |
---|---|---|
1.241.u | $2$ | (not in LMFDB) |