Sending parameters with submit doesn't work

Hi,
I’ve got very long form for submitting table search - its code is partially pasted below. As title says - submitting doesn’t send its name and value parameters. There is a code of my form:

<form action="#" phx-submit="search" id="search-form">

<%= label :city, gettext("City") %>
<%= text_input :params, :city, value: @form_vals.city %>

<%= label :range, gettext("Range") %>
<%= number_input :params, :range, value: @form_vals.range %>

... many other params ...

<%= label :page_size, gettext("Page size") %>
<%= select :params, :page_size, [5, 10, 20, 50, 100], value: @page_size %>

<%= submit gettext("Search"), value: @page_number, name: "page", phx_disable_with: gettext("Searching...") %> <br>

<%= submit gettext("Previous page"), value: @page_number+1, name: "page", phx_disable_with: gettext("Loading...") %>
Page: <%= @page_number %>, total pages: <%= @total_pages %>
<%= submit gettext("Next page"), value: @page_number-1, name: "page", phx_disable_with: gettext("Loading...") %>

</form>

The behaviour I want to achieve is to get %{"page" => number} with parameters in my liveview event handler. Rest of the parameters is passed. No clue why it doesn’t work for submit button value.