In the English Grammar Profile, C1 point 85 in the category of PAST is defined as:
invert the subject and affirmative auxiliary verb to talk about imagined situations in the past, often with regret, in formal contexts
*although a following modal verb ‘could’ or ‘would’ is not mentioned in the description above, they do follow in the EGP examples.
A search in iWeb for:
. Had _P _VVN
1 . HAD I KNOWN 1172
2 . HAD HE LIVED 141
It would have been much easier had he lived on TRAPPIST-1.
3 . HAD WE KNOWN 135
4 . HAD I GONE 101
5 . HAD I SEEN 99
6 . HAD I USED 97
7 . HAD HE KNOWN 86
8 . HAD I READ 83
9 . HAD THEY KNOWN 83
10 . HAD HE STAYED 80
11 . HAD HE GONE 65
12 . HAD I TAKEN 63
13 . HAD HE MADE 60
14 . HAD HE TAKEN 55
15 . HAD WE GONE 53
16 . HAD HE PLAYED 52
17 . HAD I THOUGHT 51
18 . HAD YOU ASKED 50
19 . HAD HE SAID 49
20 . HAD I STAYED 48
21 . HAD I REALIZED 48
22 . HAD IT TOWED 48
23 . HAD THEY GONE 47
24 . HAD I WAITED 46
25 . HAD HE WON 46
26 . HAD IT HAPPENED 45
27 . HAD HE REMAINED 44
28 . HAD SHE KNOWN 43
29 . HAD THEY KEPT 43
30 . HAD I MADE 42
31 . HAD WE USED 42
32 . HAD I TRIED 41
33 . HAD SHE LIVED 41
34 . HAD I WANTED 39
35 . HAD I KEPT 38
36 . HAD I PAID 37
37 . HAD I SAID 36
38 . HAD HE USED 36
39 . HAD I CONTINUED 36
40 . HAD I CHOSEN 36
41 . HAD THEY WON 36
42 . HAD IT GONE 34
43 . HAD WE STAYED 34
44 . HAD I FOUND 33
45 . HAD THEY MADE 33
46 . HAD YOU SEEN 32
47 . HAD I BOUGHT 31
48 . HAD I LEFT 31
49 . HAD I LISTENED 30
50 . HAD IT CHECKED 30
51 . HAD HE CONTINUED 29
52 . HAD THEY TAKEN 29
53 . HAD YOU READ 29
54 . HAD HE SEEN 28
55 . HAD HE LOST 28
56 . HAD HE SUCCEEDED 28
57 . HAD I FOLLOWED 28
58 . HAD I GIVEN 28
59 . HAD SHE WON 28
60 . HAD I GOTTEN 27
61 . HAD IT INSTALLED 27
62 . HAD THEY LOST 27
63 . HAD YOU HEARD 27
64 . HAD THEY USED 26
65 . HAD YOU BOUGHT 26
66 . HAD HE WAITED 25
67 . HAD I STARTED 25
68 . HAD WE TAKEN 25
69 . HAD I PURCHASED 24
70 . HAD HE CHOSEN 24
71 . HAD THEY FOLLOWED 24
72 . HAD THEY SUCCEEDED 24
73 . HAD YOU KNOWN 23
74 . HAD YOU SAID 23
75 . HAD HE SURVIVED 22
76 . HAD HE GIVEN 22
77 . HAD IT REPLACED 22
78 . HAD SHE GONE 22
79 . HAD WE KEPT 22
80 . HAD I LOST 21
81 . HAD I RECEIVED 21
82 . HAD HE LEFT 21
83 . HAD HE HIT 20
84 . HAD WE SEEN 20
85 . HAD I SPENT 19
86 . HAD HE READ 19
87 . HAD HE LOOKED 19
88 . HAD WE CHOSEN 19
89 . HAD WE MADE 19
90 . HAD HE DIED 18
91 . HAD HE DECIDED 18
92 . HAD HE KEPT 18
93 . HAD I PUT 18
94 . HAD I WRITTEN 18
95 . HAD THEY CONTINUED 18
96 . HAD THEY SEEN 18
97 . HAD WE LOST 18
98 . HAD YOU GONE 18
99 . HAD YOU TOLD 18
100 . HAD YOU USED 18
B2 vocabulary: purchased, survived