Properties

Label 2.19.am_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:  $1 - 12 x + 67 x^{2} - 228 x^{3} + 361 x^{4}$
Frobenius angles:  $\pm0.0409513241932$, $\pm0.374284657527$
Angle rank:  $1$ (numerical)
Number field:  \(\Q(\sqrt{-3}, \sqrt{7})\)
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
$A(\F_{q^r})$ 189 126441 47036052 16902759321 6117677843949 2212390187746704 798993160685911989 288443557605540195369 104127350298348762476532 37589943960696653730888201

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 8 352 6860 129700 2470688 47026222 893856608 16983689284 322687697780 6131061446752

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.