Scary card checked to you: Check or Bet?

[rudeybrad]

I'm extremely new to online poker (about 1 week on party) and quite frankly, this is more of an introductory post than a request for comments, since I think I know the answer to this question. The question is, looking at the hand history below, do I check the river and get the free showdown, or throw in a bet?

Party Poker 0.50/1 Hold'em (9 handed)

Preflop: rudey is Button with T[img]/images/graemlins/spade.gif[/img], T[img]/images/graemlins/diamond.gif[/img]. CO posts a blind of $0.50.
UTG calls, UTG+1 calls, JES1159 folds, MP1 folds, MP2 folds, MP3 folds, CO (poster) checks, rudey calls, SB raises, BB folds, UTG 3-bets, UTG+1 calls, CO folds, rudey calls, SB caps, UTG calls, UTG+1 calls, rudey calls.

Flop: (18 SB) J[img]/images/graemlins/heart.gif[/img], 6[img]/images/graemlins/heart.gif[/img], 3[img]/images/graemlins/diamond.gif[/img] <font color="blue">(3 players) </font>
SB bets, UTG calls, UTG+1 calls, rudey calls.

Turn: (11 BB) 5[img]/images/graemlins/diamond.gif[/img] <font color="blue">(3 players) </font>
SB bets, UTG calls, UTG+1 calls, rudey calls.

River: (15 BB) J[img]/images/graemlins/diamond.gif[/img] <font color="blue">(3 players) </font>
SB checks, UTG checks, UTG+1 checks, rudey checks.

Final Pot: 15 BB
<font color="#990066">Main Pot: 15 BB, between rudey, SB and UTG.</font> &gt; <font color="white">Pot won by rudey (15 BB).</font>

Results in white below: <font color="white">
SB doesn't show.
UTG doesn't show.
rudey shows Ts Td (two pair, jacks and tens).
Outcome: rudey wins 15 BB. </font>