Properties

Label 2.25.ap_dx
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:  $1 - 15 x + 101 x^{2} - 375 x^{3} + 625 x^{4}$
Frobenius angles:  $\pm0.0651474250922$, $\pm0.325607171919$
Angle rank:  $2$ (numerical)
Number field:  4.0.132741.1
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
$A(\F_{q^r})$ 337 376429 244824097 152538441525 95311795063552 59594532551290429 37252162062695608057 23283110855115667066725 14551933767292198562477017 9094949162757899359443349504

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 11 603 15671 390499 9759926 244099203 6103394231 152588195299 3814702125491 95367454132878

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.