Properties

Label 2.19.al_cq
Base Field $\F_{19}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian No

Learn more about

Invariants

Base field:  $\F_{19}$
Dimension:  $2$
L-polynomial:  $( 1 - 6 x + 19 x^{2} )( 1 - 5 x + 19 x^{2} )$
Frobenius angles:  $\pm0.258380448083$, $\pm0.305569972467$
Angle rank:  $2$ (numerical)
Jacobians:  0

This isogeny class is not simple.

Newton polygon

This isogeny class is ordinary.

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

Point counts

This isogeny class is principally polarizable, but does not contain a Jacobian.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 210 136500 49041720 17149860000 6135129011550 2212654514616000 798914175411488430 288436317711993360000 104127418499416252962840 37590011257887134458912500

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 9 377 7146 131593 2477739 47031842 893768241 16983262993 322687909134 6131072423177

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{19}$
The isogeny class factors as 1.19.ag $\times$ 1.19.af and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:
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.ab_i$2$(not in LMFDB)
2.19.b_i$2$(not in LMFDB)
2.19.l_cq$2$(not in LMFDB)