Properties

Label 2.25.am_cv
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:  $1 - 12 x + 73 x^{2} - 300 x^{3} + 625 x^{4}$
Frobenius angles:  $\pm0.0897012299332$, $\pm0.423034563267$
Angle rank:  $1$ (numerical)
Number field:  \(\Q(\sqrt{-3}, \sqrt{13})\)
Galois group:  $V_4$

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
$A(\F_{q^r})$ 387 391257 244144368 152102332521 95300542986867 59606472426119424 37254222610796449827 23283182051681277795273 14551915228364163481578864 9094947387877097889060876057

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 14 628 15626 389380 9758774 244148110 6103731830 152588661892 3814697265626 95367435521908

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.