Invariants
Base field: | $\F_{11}$ |
Dimension: | $3$ |
L-polynomial: | $( 1 - 5 x + 11 x^{2} )( 1 - 9 x + 39 x^{2} - 99 x^{3} + 121 x^{4} )$ |
$1 - 14 x + 95 x^{2} - 393 x^{3} + 1045 x^{4} - 1694 x^{5} + 1331 x^{6}$ | |
Frobenius angles: | $\pm0.100899808413$, $\pm0.228229222880$, $\pm0.366706655625$ |
Angle rank: | $3$ (numerical) |
This isogeny class is not 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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $371$ | $1696583$ | $2479542884$ | $3178760323375$ | $4178308288003696$ |
Point counts of the (virtual) curve
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $-2$ | $116$ | $1399$ | $14828$ | $161093$ | $1771337$ | $19491680$ | $214386596$ | $2358002065$ | $25937381651$ |
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 isogeny class factors as 1.11.af $\times$ 2.11.aj_bn and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is: |
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.ae_f_ad | $2$ | (not in LMFDB) |
3.11.e_f_d | $2$ | (not in LMFDB) |
3.11.o_dr_pd | $2$ | (not in LMFDB) |