Invariants
Base field: | $\F_{11}$ |
Dimension: | $3$ |
L-polynomial: | $( 1 - 6 x + 11 x^{2} )( 1 - 7 x + 30 x^{2} - 77 x^{3} + 121 x^{4} )$ |
$1 - 13 x + 83 x^{2} - 334 x^{3} + 913 x^{4} - 1573 x^{5} + 1331 x^{6}$ | |
Frobenius angles: | $\pm0.140218899004$, $\pm0.183470593443$, $\pm0.430420419745$ |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $408$ | $1733184$ | $2430016992$ | $3150068852736$ | $4191170058284808$ |
Point counts of the (virtual) curve
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $-1$ | $119$ | $1370$ | $14695$ | $161589$ | $1777112$ | $19510343$ | $214394191$ | $2357879726$ | $25937056519$ |
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.ag $\times$ 2.11.ah_be 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.ab_ab_ba | $2$ | (not in LMFDB) |
3.11.b_ab_aba | $2$ | (not in LMFDB) |
3.11.n_df_mw | $2$ | (not in LMFDB) |