Summary: We investigate \(\operatorname{sc}_7(n)\), the number of self-conjugate 7-core partitions of size \(n\). It turns out that \(\operatorname{sc}_7(n) = 0\) for \(n \equiv 7\pmod 8\). For \(n \equiv 1, 3, 5\pmod 8\), with \(n \not\equiv 5\pmod 7\), we find that \(\operatorname{sc}_7(n)\) is essentially a Hurwitz class number. Using recent work of L. Gao and H. Qin [Commun. Algebra 47, No. 11, 4605–4640 (2019; Zbl 1457.11025)], we show that \[\operatorname{sc}_7(n) = 2^{- \varepsilon ( n ) - 1} \cdot H(- D_n),\] where \(- D_n : = - 4^{\varepsilon ( n )}(7 n + 14)\) and \(\varepsilon(n) : = \frac{ 1}{ 2} \cdot(1 + ( - 1 )^{\frac{ n - 1}{ 2}})\). This fact implies several corollaries which are of interest. For example, if \(- D_n\) is a fundamental discriminant and \(p \notin \{2, 7 \}\) is a prime with \(\operatorname{ord}_p(- D_n) \leq 1\), then for every positive integer \(k\) we have \[\operatorname{sc}_7 ( ( n + 2 ) p^{2 k} - 2 ) = \operatorname{sc}_7(n) \cdot \left( 1 + \frac{ p^{k + 1} - p}{ p - 1} - \frac{ p^k - 1}{ p - 1} . \left( \frac{ - D_n}{ p} \right) \right),\eqno{(2)}\] where \((\frac{ - D_n}{ p})\) is the Legendre symbol.