Properties

Label 2.5.af_p
Base Field $\F_{5}$
Dimension $2$
$p$-rank $0$
Principally polarizable
Contains a Jacobian

Learn more about

Invariants

Base field:  $\F_{5}$
Dimension:  $2$
Weil polynomial:  $1 - 5 x + 15 x^{2} - 25 x^{3} + 25 x^{4}$
Frobenius angles:  $\pm0.2$, $\pm0.4$
Angle rank:  $0$ (numerical)
Number field:  \(\Q(\zeta_{5})\)
Galois group:  $C_4$

This isogeny class is simple.

Newton polygon

This isogeny class is supersingular.

$p$-rank:  $0$
Slopes:  $[1/2, 1/2, 1/2, 1/2]$

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
$A(\F_{q^r})$ 11 781 19151 406901 9759376 246109501 6152578751 152832422501 3808599606251 95245419909376

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 1 31 151 651 3126 15751 78751 391251 1950001 9753126

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.