Invariants
Base field: | $\F_{241}$ |
Dimension: | $1$ |
L-polynomial: | $1 - 26 x + 241 x^{2}$ |
Frobenius angles: | $\pm0.184072473348$ |
Angle rank: | $1$ (numerical) |
Number field: | \(\Q(\sqrt{-2}) \) |
Galois group: | $C_2$ |
Jacobians: | $9$ |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $216$ | $57888$ | $13998744$ | $3373481088$ | $812991764376$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $216$ | $57888$ | $13998744$ | $3373481088$ | $812991764376$ | $195930620647200$ | $47219273457028056$ | $11379844839141831168$ | $2742542606043797332824$ | $660952768067055638922528$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 9 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 \(\Q(\sqrt{-2}) \). |
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.ba | $2$ | (not in LMFDB) |