You have to create a layout file specifically for your CMS Page, such as in layout folder of your custom module,
cms_page_view_selectable_<CMS Page Identifier>_<Layout Update Name>.xml
for example if my CMS page identifier name is testing, I'll name it as cms_page_view_selectable_testing_loginform.xml and inside the file I can write code as below to get the login form and remember me option as well:
<?xml version="1.0"?>
<!--
/**
* Copyright © Magento, Inc. All rights reserved.
* See COPYING.txt for license details.
*/
-->
<page xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" layout="1column" xsi:noNamespaceSchemaLocation="urn:magento:framework:View/Layout/etc/page_configuration.xsd">
<head>
<link src="[Vendor]_[Module]::js/js_fileName.js"/>
</head>
</page>
And than go to your CMS page in admin and from there under design tab, select your option in Custom Layout Update, whatever you've named it, here I have named it loginform, so I'll select loginform inside my Custom Layout Update.