Properties

Label 2.25.ap_dy
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:  $1 - 15 x + 102 x^{2} - 375 x^{3} + 625 x^{4}$
Frobenius angles:  $\pm0.09460704416$, $\pm0.316968049676$
Angle rank:  $2$ (numerical)
Number field:  4.0.174556.1
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
$A(\F_{q^r})$ 338 377884 245539424 152731643584 95346211805858 59598984911155456 37252631167549945394 23283163813831131974400 14551941870575701453548128 9094950457913341110674535964

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 11 605 15716 390993 9763451 244117442 6103471091 152588542369 3814704249716 95367467713565

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.