Properties

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

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Invariants

Base field:  $\F_{19}$
Dimension:  $2$
L-polynomial:  $1 - 12 x + 68 x^{2} - 228 x^{3} + 361 x^{4}$
Frobenius angles:  $\pm0.0791769653548$, $\pm0.366480294854$
Angle rank:  $2$ (numerical)
Number field:  4.0.168192.4
Galois group:  $D_{4}$
Jacobians:  4

This isogeny class is simple and geometrically simple.

Newton polygon

This isogeny class is ordinary.

$p$-rank:  $2$
Slopes:  $[0, 0, 1, 1]$

Point counts

This isogeny class contains the Jacobians of 4 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 190 127300 47287390 16942611600 6121833155950 2212741065343300 799026649637951470 288447540686741606400 104127794396037832168030 37589982524610807362282500

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 8 354 6896 130006 2472368 47033682 893894072 16983923806 322689074024 6131067736674

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{19}$
The endomorphism algebra of this simple isogeny class is 4.0.168192.4.
All geometric endomorphisms are defined over $\F_{19}$.

Base change

This is a primitive isogeny class.

Twists

Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.19.m_cq$2$(not in LMFDB)