Properties

 Label 2.11.ah_be 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: $1 - 7 x + 30 x^{2} - 77 x^{3} + 121 x^{4}$ Frobenius angles: $\pm0.183470593443$, $\pm0.430420419745$ Angle rank: $2$ (numerical) Number field: 4.0.39593.1 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:

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

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 68 16048 1849328 214465472 25947340108 3144123903232 380029698717212 45951475832008448 5559601338333581552 672737920931822176048

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 5 133 1388 14649 161115 1774774 19501529 214367025 2357813684 25936959093

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{11}$
 The endomorphism algebra of this simple isogeny class is 4.0.39593.1.
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.h_be $2$ 2.121.l_cm