Properties

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

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Invariants

Base field:  $\F_{5}$
Dimension:  $2$
Weil polynomial:  $1 - 6 x + 17 x^{2} - 30 x^{3} + 25 x^{4}$
Frobenius angles:  $\pm0.0512862249088$, $\pm0.384619558242$
Angle rank:  $1$ (numerical)
Number field:  \(\Q(\sqrt{2}, \sqrt{-3})\)
Galois group:  $C_2^2$

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
$A(\F_{q^r})$ 7 553 15484 363321 9198847 239754256 6109689607 152926532073 3814701058588 95315867737993

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 0 24 126 580 2940 15342 78204 391492 1953126 9760344

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.