Properties

 Label 3.11.an_db_aly Base Field $\F_{11}$ Dimension $3$ Ordinary Yes $p$-rank $3$ Principally polarizable Yes Contains a Jacobian No

Invariants

 Base field: $\F_{11}$ Dimension: $3$ L-polynomial: $( 1 - 6 x + 11 x^{2} )( 1 - 7 x + 26 x^{2} - 77 x^{3} + 121 x^{4} )$ Frobenius angles: $\pm0.0895839137776$, $\pm0.140218899004$, $\pm0.469832509767$ Angle rank: $3$ (numerical)

This isogeny class is not simple.

Newton polygon

This isogeny class is ordinary.

 $p$-rank: $3$ Slopes: $[0, 0, 0, 1, 1, 1]$

Point counts

This isogeny class is principally polarizable, but does not contain a Jacobian.

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 384 1603584 2281019904 3078522077184 4176699208201344 5575298046411571200 7406968087636782820224 9850850807949927939833856 13110397656412088165171129856 17449799457834088098969972455424

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ -1 111 1286 14359 161029 1776456 19504855 214383215 2358020258 25938014991

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{11}$
 The isogeny class factors as 1.11.ag $\times$ 2.11.ah_ba and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:
All geometric endomorphisms are defined over $\F_{11}$.

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_af_c $2$ (not in LMFDB) 3.11.b_af_ac $2$ (not in LMFDB) 3.11.n_db_ly $2$ (not in LMFDB)