Properties

Label 1.25.aj
Base Field $\F_{5^2}$
Dimension $1$
Ordinary No
$p$-rank $1$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{5^2}$
Dimension:  $1$
Weil polynomial:  $1 - 9 x + 25 x^{2}$
Frobenius angles:  $\pm0.143566293129$
Angle rank:  $1$ (numerical)
Number field:  \(\Q(\sqrt{-19}) \)
Galois group:  $C_2$

This isogeny class is simple.

Newton polygon

This isogeny class is ordinary.

$p$-rank:  $1$
Slopes:  $[0, 1]$

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
$A(\F_{q^r})$ 17 595 15572 390915 9769577 244168960 6103671857 152588588355 3814699639412 95367435561475

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 17 595 15572 390915 9769577 244168960 6103671857 152588588355 3814699639412 95367435561475

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.