Properties

Label 2.25.au_fu
Base Field $\F_{5^2}$
Dimension $2$
$p$-rank $0$
Principally polarizable
Contains a Jacobian

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Invariants

Base field:  $\F_{5^2}$
Dimension:  $2$
Weil polynomial:  $( 1 - 5 x )^{4}$
Frobenius angles:  $0.0$, $0.0$, $0.0$, $0.0$
Angle rank:  $0$ (numerical)

Newton polygon

This isogeny class is supersingular.

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

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
$A(\F_{q^r})$ 256 331776 236421376 151613669376 95245419909376 59589387451109376 37250995672607109376 23282825947723387109376 14551885426067352287109376 9094943292439556121787109376

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 6 526 15126 388126 9753126 244078126 6103203126 152586328126 3814689453126 95367392578126

Decomposition

1.25.ak 2

Base change

This isogeny class is not primitive. It is a base change from the following isogeny classes over subfields of $\F_{5^2}$.

SubfieldPrimitive Model
$\F_{5}$2.5.a_ak