Properties

Label 2.25.am_cy
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:  $1 - 12 x + 76 x^{2} - 300 x^{3} + 625 x^{4}$
Frobenius angles:  $\pm0.131218376688$, $\pm0.408414038432$
Angle rank:  $2$ (numerical)
Number field:  4.0.2361600.2
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
$A(\F_{q^r})$ 390 395460 245843910 152427684240 95335675119750 59609451785553540 37254687124607709510 23283261709234306191360 14551919970753601877719590 9094946256148610278912666500

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 14 634 15734 390214 9762374 244160314 6103807934 152589183934 3814698508814 95367423654874

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.