Properties

Label 2.25.ao_do
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:  $1 - 14 x + 92 x^{2} - 350 x^{3} + 625 x^{4}$
Frobenius angles:  $\pm0.0849786306216$, $\pm0.356598155418$
Angle rank:  $2$ (numerical)
Number field:  4.0.442176.2
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
$A(\F_{q^r})$ 354 383028 245223234 152465061456 95305798099794 59597974337790996 37253171563634889426 23283234873186725680128 14551938035580978069408018 9094948293446947741852666068

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 12 614 15696 390310 9759312 244113302 6103559628 152589008062 3814703244396 95367445017494

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.