Properties

Label 2.19.am_cu
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:  $1 - 12 x + 72 x^{2} - 228 x^{3} + 361 x^{4}$
Frobenius angles:  $\pm0.176318466621$, $\pm0.323681533379$
Angle rank:  $1$ (numerical)
Number field:  \(\Q(\zeta_{8})\)
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
$A(\F_{q^r})$ 194 130756 48296882 17097131536 6135495123074 2213314831134724 799010429326500914 288443868954489667584 104127604530951176173442 37589973457544943538923076

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 8 362 7040 131190 2477888 47045882 893875928 16983707614 322688485640 6131066257802

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.