Properties

Label 2.19.al_cp
Base Field $\F_{19}$
Dimension $2$
$p$-rank $2$
Principally polarizable
Contains a Jacobian

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Invariants

Base field:  $\F_{19}$
Dimension:  $2$
Weil polynomial:  $1 - 11 x + 67 x^{2} - 209 x^{3} + 361 x^{4}$
Frobenius angles:  $\pm0.225619498788$, $\pm0.332359937866$
Angle rank:  $2$ (numerical)
Number field:  4.0.45725.1
Galois group:  $D_4$

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
$A(\F_{q^r})$ 209 135641 48809651 17121827789 6134444175024 2212955922576641 798965794289625479 288439911158049053909 104127351848432066042141 37589968388064876490181376

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 9 375 7113 131379 2477464 47038251 893825991 16983474579 322687702587 6131065430950

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.