Properties

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

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Invariants

Base field:  $\F_{11}$
Dimension:  $2$
Weil polynomial:  $1 - 9 x + 41 x^{2} - 99 x^{3} + 121 x^{4}$
Frobenius angles:  $\pm0.178435994483$, $\pm0.329700688269$
Angle rank:  $2$ (numerical)
Number field:  \(\Q(\zeta_{5})\)
Galois group:  $C_4$

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
$A(\F_{q^r})$ 55 14905 1882705 218522205 26001250000 3138320501305 379774219636405 45953777683469205 5560070301147558955 672748459337020000000

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 3 123 1413 14923 161448 1771503 19488423 214377763 2358012573 25937365398

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.