Invariants
Base field: | $\F_{11}$ |
Dimension: | $3$ |
L-polynomial: | $1 - 14 x + 94 x^{2} - 387 x^{3} + 1034 x^{4} - 1694 x^{5} + 1331 x^{6}$ |
Frobenius angles: | $\pm0.0887296077117$, $\pm0.207434636458$, $\pm0.384783505598$ |
Angle rank: | $3$ (numerical) |
Number field: | 6.0.59264075.1 |
Galois group: | $A_4\times C_2$ |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $365$ | $1662575$ | $2435836625$ | $3154139198075$ | $4174009280277875$ |
Point counts of the (virtual) curve
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $-2$ | $114$ | $1375$ | $14714$ | $160928$ | $1772241$ | $19496818$ | $214391154$ | $2357948500$ | $25937127374$ |
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 6.0.59264075.1. |
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.o_dq_ox | $2$ | (not in LMFDB) |