Properties

Label 2.5.ad_e
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:  $1 - 3 x + 4 x^{2} - 15 x^{3} + 25 x^{4}$
Frobenius angles:  $\pm0.0673911931187$, $\pm0.599275473548$
Angle rank:  $1$ (numerical)
Number field:  \(\Q(\sqrt{-3}, \sqrt{-11})\)
Galois group:  $V_4$

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
$A(\F_{q^r})$ 12 576 11664 361728 9943932 241864704 6064084668 153038435328 3818287953936 95338124237376

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 3 25 90 577 3183 15478 77619 391777 1954962 9762625

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.