Properties

Label 2.11.ah_z
Base Field $\F_{11}$
Dimension $2$
$p$-rank $2$
Principally polarizable
Contains a Jacobian

Learn more about

Invariants

Base field:  $\F_{11}$
Dimension:  $2$
Weil polynomial:  $1 - 7 x + 25 x^{2} - 77 x^{3} + 121 x^{4}$
Frobenius angles:  $\pm0.053038025356$, $\pm0.477974681599$
Angle rank:  $2$ (numerical)
Number field:  4.0.72557.1
Galois group:  $D_4$

This isogeny class is simple.

Newton polygon

This isogeny class is ordinary.

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

Point counts

This isogeny class contains a Jacobian, and hence is principally polarizable.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 63 14553 1707993 208238877 25807119408 3140194662297 379762271603757 45942912351151893 5559767463949717347 672757224167283349248

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 5 123 1283 14219 160240 1772559 19487809 214327075 2357884139 25937703318

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.