Properties

Label 2.25.an_de
Base Field $\F_{5^2}$
Dimension $2$
$p$-rank $2$
Principally polarizable
Contains a Jacobian

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Invariants

Base field:  $\F_{5^2}$
Dimension:  $2$
Weil polynomial:  $1 - 13 x + 82 x^{2} - 325 x^{3} + 625 x^{4}$
Frobenius angles:  $\pm0.0779611327259$, $\pm0.393003920309$
Angle rank:  $2$ (numerical)
Number field:  4.0.880844.1
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
$A(\F_{q^r})$ 370 387020 244538920 152207225600 95286087384850 59600582806242560 37253716054725697330 23283216743677214182400 14551922319598103022291880 9094946633634471428935745100

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 13 621 15652 389649 9757293 244123986 6103648837 152588889249 3814699124548 95367427613101

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.