Properties

Label 2.25.as_fb
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:  $( 1 - 9 x + 25 x^{2} )^{2}$
Frobenius angles:  $\pm0.143566293129$, $\pm0.143566293129$
Angle rank:  $1$ (numerical)

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
$A(\F_{q^r})$ 289 354025 242487184 152814537225 95444634758929 59618481027481600 37254810137933828449 23283277296171641606025 14551933338930042823705744 9094947765572086448504175625

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 8 564 15518 391204 9773528 244197294 6103828088 152589286084 3814702013198 95367439482324

Decomposition

1.25.aj 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_aj