Properties

Label 2.25.aq_ei
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:  $1 - 16 x + 112 x^{2} - 400 x^{3} + 625 x^{4}$
Frobenius angles:  $\pm0.109490882418$, $\pm0.271157989061$
Angle rank:  $2$ (numerical)
Number field:  4.0.41216.1
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
$A(\F_{q^r})$ 322 371588 245395234 152964943376 95403234965122 59605293521677316 37252706006959595362 23283071884126425448448 14551927341103578433921858 9094949947108970491607060868

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 10 594 15706 391590 9769290 244143282 6103483354 152587939902 3814700440906 95367462357394

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.