Properties

Label 2.25.ao_dt
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:  $1 - 14 x + 97 x^{2} - 350 x^{3} + 625 x^{4}$
Frobenius angles:  $\pm0.181719349551$, $\pm0.311346897918$
Angle rank:  $2$ (numerical)
Number field:  4.0.128576.2
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
$A(\F_{q^r})$ 359 390233 248555804 153258937721 95415159378519 59604985225836176 37252722941774050391 23283078169705691603753 14551921189520482934528348 9094947199453530582488933193

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 12 624 15906 392340 9770512 244142022 6103486128 152587981092 3814698828306 95367433546144

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.