Properties

Label 2.25.an_dd
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:  $1 - 13 x + 81 x^{2} - 325 x^{3} + 625 x^{4}$
Frobenius angles:  $\pm0.0544401465072$, $\pm0.398133042327$
Angle rank:  $2$ (numerical)
Number field:  4.0.6525.1
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
$A(\F_{q^r})$ 369 385605 243924129 152070658245 95266422092304 59598081227842245 37253302812836762769 23283140005390547056005 14551910907951479309927649 9094945417268223266468352000

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 13 619 15613 389299 9755278 244113739 6103581133 152588386339 3814696133053 95367414858574

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.