I don't know where you got those "Quenya" lines but they look suspiciously like from a certain broken machine translator which is absolutely not helpful.
I'd use corma for "ring" - cor would be Sindarin. (cf. Cormacolindor "Ring-bearers")
Er corma "One ring" sounds about right.
Now "to show" is to explain the purpose or attribute of "One ring". AFAIK, the only known sample from the corpus that comes close is
Vanda sina termaruva Elenna-nóreo alcar enyalien
Oath this stand-FUT Star-wards-land-GEN glory recall-GERUND-DATIVE.
"This oath shall stand in memory of the glory of the Land of the Star"
Or literally "This oath shall stand for the recalling of/to recall ..."
This would lead to: Er corma tanien <our love>.
**mel from your translation would be the bare stem of the verb "to love". No, you can't use a verb here, let alone its stem. The noun is melme.
So depending on who WE are, our love can be translated:
melmelva "our love (mine, yours, and others')"
melmelma "our love (ours, not yours)"
Or let's say it should be:
melmenqua "our love (between you and me, the two of us)"
The first line would then be:
Er corma tanien melmenqua.
the third:
Er corma palien calanqua.
And The fourth:
ar ullume carien inque calima
and forever make-GERUND-DATIVE us/thee-and-me bright
Or:
ar ullume calimatien inque
and forever bright-CAUSATIVE-GERUND-DATIVE us/thee-and-me
The second line is tricky because I can't find a word for "seal". Maybe you can find a replacement with a real dictionary.
Alternatively, instead of using the dative form of a gerund, you can use a relative clause, which is far better attested in Quenya.
Er corma i tana melmenqua One ring that shows our love.
??
Er corma i palya calanqua One ring that spreads our light
Ar ullume calmata inque ~
I found a fan-coined verb *lihta- "to seal" (from líco "wax"), it looks OK, IMO.
The second line can therefore be either:
Er corma lihtien melmenqua
or
Er corma i lihta melmenqua