Properties

 Label 2.11.ah_bc Base field $\F_{11}$ Dimension $2$ $p$-rank $2$ Ordinary Yes Supersingular No Simple No Geometrically simple No Primitive Yes Principally polarizable Yes Contains a Jacobian Yes

Invariants

 Base field: $\F_{11}$ Dimension: $2$ L-polynomial: $( 1 - 6 x + 11 x^{2} )( 1 - x + 11 x^{2} )$ Frobenius angles: $\pm0.140218899004$, $\pm0.451829325548$ Angle rank: $2$ (numerical) Jacobians: 3

This isogeny class is not simple.

Newton polygon

This isogeny class is ordinary.

 $p$-rank: $2$ Slopes: $[0, 0, 1, 1]$

Point counts

This isogeny class contains the Jacobians of 3 curves, and hence is principally polarizable:

• $y^2=6x^6+4x^5+3x^4+7x^3+8x^2+2$
• $y^2=6x^6+2x^5+5x^4+4x^3+6x^2+5x+7$
• $y^2=10x^6+10x+8$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 66 15444 1792296 212138784 25925084526 3145479480000 380071732087806 45953341316049024 5559849011620762056 672753001834059172884

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 5 129 1346 14489 160975 1775538 19503685 214375729 2357918726 25937540529

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{11}$
 The isogeny class factors as 1.11.ag $\times$ 1.11.ab 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 2.11.af_q $2$ 2.121.h_aca 2.11.f_q $2$ 2.121.h_aca 2.11.h_bc $2$ 2.121.h_aca