Properties

Label 2.25.am_da
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:  $1 - 12 x + 78 x^{2} - 300 x^{3} + 625 x^{4}$
Frobenius angles:  $\pm0.155626651349$, $\pm0.397271686086$
Angle rank:  $2$ (numerical)
Number field:  4.0.31744.1
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
$A(\F_{q^r})$ 392 398272 246979208 152636947456 95353241558792 59609382226792384 37254555871388553992 23283250986546941902848 14551916305720182652500104 9094944834381074982354231232

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 14 638 15806 390750 9764174 244160030 6103786430 152589113662 3814697548046 95367408746558

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.