Properties

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

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Invariants

 Base field: $\F_{11}$ Dimension: $3$ L-polynomial: $( 1 - 6 x + 11 x^{2} )( 1 - 10 x + 45 x^{2} - 110 x^{3} + 121 x^{4} )$ Frobenius angles: $\pm0.0820279942768$, $\pm0.140218899004$, $\pm0.318205720493$ 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 $A(\F_{q^r})$ 282 1456812 2361378888 3155955935328 4177922312632602 5559031135945425600 7401838896556089732462 9851807652998016288240000 13111220218893013578817121688 17449833087139019509072187916012

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ -4 98 1334 14722 161076 1771280 19491356 214404034 2358168194 25938064978

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{11}$
 The isogeny class factors as 1.11.ag $\times$ 2.11.ak_bt 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.ae_ae_by $2$ (not in LMFDB) 3.11.e_ae_aby $2$ (not in LMFDB) 3.11.q_em_sw $2$ (not in LMFDB)