# Properties

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

## 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.

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

 $r$ 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.
 Twist Extension Degree Common 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)