Properties

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

Invariants

 Base field: $\F_{5^2}$ Dimension: $1$ Weil polynomial: $1 + 9 x + 25 x^{2}$ Frobenius angles: $\pm0.856433706871$ 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.

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 35 595 15680 390915 9761675 244168960 6103359395 152588588355 3814694891840 95367435561475

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 35 595 15680 390915 9761675 244168960 6103359395 152588588355 3814694891840 95367435561475

Decomposition

This is a simple isogeny class.

Base change

This isogeny class is not primitive. It is a base change from the following isogeny classes over subfields of $\F_{5^2}$.

 Subfield Primitive Model $\F_{5}$ 1.5.ab $\F_{5}$ 1.5.b