Properties

 Label 2.11.aj_bo 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: $( 1 - 6 x + 11 x^{2} )( 1 - 3 x + 11 x^{2} )$ Frobenius angles: $\pm0.140218899004$, $\pm0.350615407277$ Angle rank: $2$ (numerical) Jacobians: 2

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 2 curves, and hence is principally polarizable:

• $y^2=3x^6+5x^5+9x^4+3x^3+6x^2+7x+10$
• $y^2=10x^6+4x^4+10x^3+5x^2+8x+7$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 54 14580 1844856 216133920 25921530954 3138100056000 379897009061274 45960688754686080 5560275246183319896 672752360451014464500

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 3 121 1386 14761 160953 1771378 19494723 214410001 2358099486 25937515801

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{11}$
 The isogeny class factors as 1.11.ag $\times$ 1.11.ad 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.ad_e $2$ 2.121.ab_ci 2.11.d_e $2$ 2.121.ab_ci 2.11.j_bo $2$ 2.121.ab_ci