Properties

Label 2.25.an_df
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:  $1 - 13 x + 83 x^{2} - 325 x^{3} + 625 x^{4}$
Frobenius angles:  $\pm0.096775394937$, $\pm0.387586574437$
Angle rank:  $2$ (numerical)
Number field:  4.0.1080141.1
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
$A(\F_{q^r})$ 371 388437 245154203 152342272341 95304484355696 59602581903675069 37253999324421141899 23283268113843463658373 14551929470680753036864139 9094947148032695703498700032

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 13 623 15691 389995 9759178 244132175 6103695247 152589225907 3814700999161 95367433006958

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.