You can solve this using an online ASN.1 parser (or openssl asn1parse), where you will find out that the base 64 string - the text in the middle, between the lines starting with ---
- is an ASN.1 encoding of the private key. The second element within the SEQUENCE - which has been altered - contains the modulus, not the private exponent. The structure is defined in PKCS#1, which is a rather readable standard, also copied in RFC 3447
The modulus is normally public, but if you haven't got the public key, you can still recreate it: How to factor RSA modulus given the public and private exponent?