Properties

Label 2.25.am_ct
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:  $1 - 12 x + 71 x^{2} - 300 x^{3} + 625 x^{4}$
Frobenius angles:  $\pm0.0507874282237$, $\pm0.431773756119$
Angle rank:  $2$ (numerical)
Number field:  4.0.867600.5
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
$A(\F_{q^r})$ 385 388465 243013540 151877772585 95271264174625 59602396082281360 37253436116030183665 23283046875737541819465 14551899270460142117309860 9094946054594511641712576625

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 14 624 15554 388804 9755774 244131414 6103602974 152587776004 3814693082354 95367421541424

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.