Properties

Label 2.25.am_cu
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:  $1 - 12 x + 72 x^{2} - 300 x^{3} + 625 x^{4}$
Frobenius angles:  $\pm0.0725107809371$, $\pm0.427489219063$
Angle rank:  $1$ (numerical)
Number field:  \(\Q(i, \sqrt{14})\)
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
$A(\F_{q^r})$ 386 389860 243578738 151990819600 95286489448466 59604645223591780 37253879096039955938 23283123720588365414400 14551908880055858609511746 9094947017729312089039363300

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 14 626 15590 389094 9757334 244140626 6103675550 152588279614 3814695601454 95367431640626

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.