# Properties

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

## Invariants

 Base field: $\F_{11}$ Dimension: $2$ L-polynomial: $1 - 6 x + 24 x^{2} - 66 x^{3} + 121 x^{4}$ Frobenius angles: $\pm0.175918430288$, $\pm0.482992569757$ Angle rank: $2$ (numerical) Number field: 4.0.417088.1 Galois group: $D_{4}$ Jacobians: 4

This isogeny class is simple and geometrically 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 4 curves, and hence is principally polarizable:

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

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 74 16132 1798274 213006928 26023590434 3147558544228 379941296838506 45945819304915968 5559752173395934586 672751109502512533732

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 6 134 1350 14550 161586 1776710 19496994 214340638 2357877654 25937467574

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{11}$
 The endomorphism algebra of this simple isogeny class is 4.0.417088.1.
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.g_y $2$ 2.121.m_ba