Properties

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

Learn more about

Invariants

Base field:  $\F_{5^2}$
Dimension:  $2$
Weil polynomial:  $( 1 - 8 x + 25 x^{2} )^{2}$
Frobenius angles:  $\pm0.204832764699$, $\pm0.204832764699$
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
$A(\F_{q^r})$ 324 374544 246929796 153413222400 95489208772164 59616123355313424 37253296650209919876 23282963759721716121600 14551888956352647673121604 9094943335293093538438738704

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 10 598 15802 392734 9778090 244187638 6103580122 152587231294 3814690378570 95367393027478

Decomposition

1.25.ai 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_ai