`perfect_power()` gives wrong result

[maxale]

Steps To Reproduce

sage: (26^2).perfect_power()
(676, 1)

Expected Behavior

Should return(26, 2).

Actual Behavior

Wrong result.

Additional Information

No response

Environment

• OS: Ubuntu 24.04.3 LTS
• Sage Version: 10.7.beta8

Checklist

• I have searched the existing issues for a bug report that matches the one I want to file, without success.
• I have read the documentation and troubleshoot guide

[fchapoton]

indeed, strange

sage: g=26^2
sage: g.perfect_power()
(676, 1)
sage: g.__pari__().ispower()
(2, 26)

so it must be following another branch in the code

[vincentmacri]

A few other failures: 36, 100, 196, 400, 576.

[fchapoton]

This goes through the lines

                if n < 1000:
                    if _small_primes_table[n >> 1]:
                        return self, one

[fchapoton]

should be fixed by

-                if n < 1000:
+                elif n < 1000: