Properties

Label 2.25.an_dk
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:  $1 - 13 x + 88 x^{2} - 325 x^{3} + 625 x^{4}$
Frobenius angles:  $\pm0.1728466634$, $\pm0.353614178508$
Angle rank:  $2$ (numerical)
Number field:  4.0.154904.1
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
$A(\F_{q^r})$ 376 395552 248238208 152994766976 95377453936696 59605143387183104 37253582749969222264 23283209683111114408448 14551925155511535037454464 9094945581649236494308172832

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 13 633 15886 391665 9766653 244142670 6103626997 152588842977 3814699867966 95367416582233

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.