One is correct. 1944.
1957 and 1973 were undefeated, but not 'perfect' seasons.
And the AP poll was taken after the 1971 Rose Bowl, in case somebody was thinking 1970 could be included if the only loss was after the last AP poll.
What about 1961? 8-0-1
1957 - lost to TCU in the first game
<TABLE border=1><TBODY><TR><TD bgColor=#c0c0c0 colSpan=8>
1957-Ohio State (Big Ten)
</TD></TR><TR><TD align=right bgColor=#00ff00>9/28</TD><TD bgColor=#00ff00>vs.</TD><TD bgColor=#00ff00>
Texas Christian (5-4-1)</TD><TD bgColor=#00ff00>L</TD><TD align=right bgColor=#00ff00>14</TD><TD align=right bgColor=#00ff00>18</TD></TR><TR><TD align=right bgColor=#00ff00>10/5</TD><TD bgColor=#00ff00>@</TD><TD bgColor=#00ff00>
Washington (3-6-1)</TD><TD bgColor=#00ff00>W</TD><TD align=right bgColor=#00ff00>35</TD><TD align=right bgColor=#00ff00>7</TD></TR><TR><TD align=right bgColor=#00ff00>10/12</TD><TD bgColor=#00ff00>vs.</TD><TD bgColor=#00ff00>
*Illinois (4-5)</TD><TD bgColor=#00ff00>W</TD><TD align=right bgColor=#00ff00>21</TD><TD align=right bgColor=#00ff00>7</TD></TR><TR><TD align=right bgColor=#00ff00>10/19</TD><TD bgColor=#00ff00>vs.</TD><TD bgColor=#00ff00>
*Indiana (1-8)</TD><TD bgColor=#00ff00>W</TD><TD align=right bgColor=#00ff00>56</TD><TD align=right bgColor=#00ff00>0</TD></TR><TR><TD align=right bgColor=#00ff00>10/26</TD><TD bgColor=#00ff00>@</TD><TD bgColor=#00ff00>
*Wisconsin (6-3)</TD><TD bgColor=#00ff00>W</TD><TD align=right bgColor=#00ff00>16</TD><TD align=right bgColor=#00ff00>13</TD></TR><TR><TD align=right bgColor=#00ff00>11/2</TD><TD bgColor=#00ff00>vs.</TD><TD bgColor=#00ff00>
*Northwestern (0-9)</TD><TD bgColor=#00ff00>W</TD><TD align=right bgColor=#00ff00>47</TD><TD align=right bgColor=#00ff00>6</TD></TR><TR><TD align=right bgColor=#00ff00>11/9</TD><TD bgColor=#00ff00>vs.</TD><TD bgColor=#00ff00>
*Purdue (5-4)</TD><TD bgColor=#00ff00>W</TD><TD align=right bgColor=#00ff00>20</TD><TD align=right bgColor=#00ff00>7</TD></TR><TR><TD align=right bgColor=#00ff00>11/16</TD><TD bgColor=#00ff00>vs.</TD><TD bgColor=#00ff00>
*Iowa (7-1-1)</TD><TD bgColor=#00ff00>W</TD><TD align=right bgColor=#00ff00>17</TD><TD align=right bgColor=#00ff00>13</TD></TR><TR><TD align=right bgColor=#00ff00>11/23</TD><TD bgColor=#00ff00>@</TD><TD bgColor=#00ff00>
*Michigan (5-3-1)</TD><TD bgColor=#00ff00>W</TD><TD align=right bgColor=#00ff00>31</TD><TD align=right bgColor=#00ff00>14</TD></TR><TR><TD align=right bgColor=#00ff00>1/1</TD><TD bgColor=#00ff00>vs.</TD><TD bgColor=#00ff00>
Oregon (7-4)</TD><TD bgColor=#00ff00>W</TD><TD align=right bgColor=#00ff00>10</TD><TD align=right bgColor=#00ff00>7</TD><TD bgColor=#00ff00>@ Pasadena, CA</TD><TD bgColor=#00ff00>Rose Bowl</TD></TR><TR><TD bgColor=#c0c0c0 colSpan=2></TD><TD bgColor=#c0c0c0>
9-1-0
</TD><TD bgColor=#c0c0c0></TD><TD bgColor=#c0c0c0>267</TD><TD bgColor=#c0c0c0>92</TD></TR></TBODY></TABLE>