Invariants
Base field: | $\F_{11}$ |
Dimension: | $3$ |
L-polynomial: | $1 - 13 x + 76 x^{2} - 291 x^{3} + 836 x^{4} - 1573 x^{5} + 1331 x^{6}$ |
Frobenius angles: | $\pm0.0354721676546$, $\pm0.103262097857$, $\pm0.494210615205$ |
Angle rank: | $3$ (numerical) |
Number field: | 6.0.2343728.1 |
Galois group: | $S_4\times C_2$ |
This isogeny class is simple and geometrically simple, primitive, ordinary, and not supersingular. It is principally polarizable.
Newton polygon
This isogeny class is ordinary.
$p$-rank: | $3$ |
Slopes: | $[0, 0, 0, 1, 1, 1]$ |
Point counts
Point counts of the abelian variety
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $367$ | $1512407$ | $2178396028$ | $3027725383475$ | $4158835374916837$ |
Point counts of the (virtual) curve
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $-1$ | $105$ | $1226$ | $14117$ | $160339$ | $1773096$ | $19487705$ | $214336533$ | $2357974370$ | $25937919845$ |
Jacobians and polarizations
This isogeny class is principally polarizable, but does not contain a Jacobian.
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{11}$.
Endomorphism algebra over $\F_{11}$The endomorphism algebra of this simple isogeny class is 6.0.2343728.1. |
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 |
---|---|---|
3.11.n_cy_lf | $2$ | (not in LMFDB) |