Properties

Label 2.25.am_cw
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:  $1 - 12 x + 74 x^{2} - 300 x^{3} + 625 x^{4}$
Frobenius angles:  $\pm0.104680351346$, $\pm0.418388652673$
Angle rank:  $2$ (numerical)
Number field:  4.0.35136.1
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
$A(\F_{q^r})$ 388 392656 244710436 152212313088 95313424978468 59607880627658704 37254469736355804292 23283223447359075729408 14551918846847862658349764 9094947299895065809912896976

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 14 630 15662 389662 9760094 244153878 6103772318 152588933182 3814698214190 95367434599350

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.