1
def dembelle_curves():
2
    F = NumberField(x**2 - x - 1, 'w')
3
    w = F.gen()
4
    v = [
5
    [ w + 1, -w - 1, w, -2, -w + 1 ],
6
    [ 0, w - 1, w + 1, 0, -w ],
7
    [ 0, -w + 1, 1, 1, 0 ],
8
    [ w + 1, -1, 0, -2*w - 1, 0 ],
9
    [ w, w + 1, 0, w + 1, 0 ],
10
    [ w, w + 1, w + 1, 2*w - 2, -w + 1 ],
11
    [ w + 1, w - 1, 0, 2, w - 1 ],
12
    [ w, w - 1, 1, 0, 0 ],
13
    [ 0, 1, 1, -2*w - 1, 2*w + 1 ],
14
    [ 1, -1, w + 1, -w - 2, -w - 1 ],
15
    [ 1, -w, w, w - 2, -w + 1 ],
16
    [ 1, -w, w, -w, 0 ],
17
    [ w + 1, -1, w, -2*w - 1, 0 ],
18
    [ w, -w - 1, 1, 0, 0 ],
19
    [ w + 1, 0, w, -w - 2, w - 2 ],
20
    [ 1, w - 1, w, -1, -w + 1 ],
21
    [ 1, w, w, 0, 0 ],
22
    [ 1, -1, 1, -1, 0 ],
23
    [ 0, -w - 1, w + 1, 0, 0 ],
24
    [ 0, 0, w, -w - 1, 0 ],
25
    [ 0, 1, w + 1, 2*w - 3, -2*w + 1 ],
26
    [ 1, -w, 1, 0, 0 ],
27
    [ 1, -w - 1, w + 1, 0, -w ],
28
    [ w + 1, w + 1, w + 1, 3*w + 1, 3*w + 2 ],
29
    [ 1, w - 1, 1, -w, 0 ],
30
    [ w, 1, w + 1, -2, -w ],
31
    [ 0, w, w + 1, w - 1, -w ],
32
    [ w + 1, -w, w + 1, -2*w - 1, 0 ],
33
    [ 0, w + 1, w + 1, 2*w + 1, 0 ],
34
    [ 0, -w, w, w - 1, -w + 1 ],
35
    [ 1, -w - 1, w, w - 1, -1 ],
36
    [ w + 1, w - 1, w + 1, -w - 1, -w ],
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    [ w + 1, w + 1, 0, 2*w + 1, 0 ],
38
    [ w, -w + 1, w, -2*w + 2, -w + 1 ],
39
    [ w, w, 0, w, -w + 2 ],
40
    [ 0, 1, w, w + 1, 0 ],
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    [ 1, -w - 1, 1, -w - 1, 2*w + 1 ],
42
    [ 0, -w - 1, w, -2, -1 ],
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    [ 1, 0, w + 1, -1, -w ],
44
    [ 1, w - 1, w, -w + 1, -w + 1 ],
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    [ 0, w + 1, w + 1, 1, -w ],
46
    [ w, w - 1, 0, -2*w - 2, w + 2 ],
47
    [ w + 1, 1, 1, -w - 2, 0 ],
48
    [ w, -w + 1, 0, -w, 0 ],
49
    [ 1, w, 0, -2*w - 2, w + 1 ],
50
    [ w + 1, 1, 0, -2*w - 1, 0 ],
51
    [ 1, 0, w + 1, -w - 1, 0 ],
52
    [ w + 1, -1, 0, -2*w, w ],
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    [ w, w, w + 1, w - 2, -2*w + 2 ],
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    [ 0, w + 1, w + 1, -2*w - 1, 0 ],
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    [ w + 1, 0, w + 1, -3*w - 2, 0 ],
56
    [ w + 1, w + 1, 1, 2*w + 1, w ],
57
    [ 1, w, 1, -w - 1, 2*w - 3 ],
58
    [ w, 1, w, -3*w - 3, 2*w ],
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    [ w, -w - 1, w + 1, -1, -w ],
60
    [ w + 1, -w - 1, w + 1, -2*w - 2, 0 ],
61
    [ 0, w - 1, w + 1, -w + 1, -w ],
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    [ 1, -w - 1, 1, w, 2*w + 1 ],
63
    [ w + 1, -1, w, -w - 1, -1 ],
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    [ 1, w - 1, 1, -3*w - 2, 2*w + 1 ],
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    [ w, -1, w, 3*w + 2, -3*w - 2 ],
66
    [ 0, w + 1, w + 1, w - 1, -w ],
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    [ w + 1, 0, 1, -w - 2, -2*w - 2 ],
68
    [ 0, w + 1, 1, 2*w + 1, 2*w + 1 ],
69
    [ w, 0, 1, -3*w + 3, 0 ],
70
    [ 1, w - 1, 0, -3*w - 1, 2*w + 1 ],
71
    [ 0, -w, 1, 2*w - 2, -w + 1 ],
72
    [ 1, 1, w, -2*w + 2, -w + 1 ],
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    [ w + 1, -w + 1, 0, 2*w - 3, 0 ],
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    [ 1, -w + 1, w, -w + 1, -w + 1 ],
75
    [ 1, 0, w, -w, -1 ],
76
    [ w + 1, w - 1, 0, w, 0 ],
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    [ 0, 0, 1, -3*w - 2, 2*w + 1 ],
78
    [ 0, 1, 1, -3, 1 ],
79
    [ 0, -w + 1, 1, -w + 1, 0 ],
80
    [ w + 1, w, w + 1, w - 3, -3 ],
81
    [ w, -w, 1, 3*w + 1, -3*w - 3 ],
82
    [ 0, -1, w + 1, w, -w ],
83
    [ 0, -1, w + 1, -3*w - 1, 2*w + 3 ],
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    [ w + 1, 0, w + 1, -2*w - 1, -w ],
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    [ w + 1, -1, 1, -3*w - 2, 2*w + 1 ],
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    [ w + 1, w - 1, 0, -3*w - 1, -3*w - 2 ],
87
    [ w, 1, 1, -2*w + 1, 0 ],
88
    [ 1, -1, 1, -3*w - 3, -2*w - 1 ],
89
    [ 1, -w + 1, 0, -w, 0 ],
90
    [ w, w, w + 1, 0, -1 ],
91
    [ 1, w - 1, 1, -1, -w ],
92
    [ 0, -w + 1, 1, w - 2, 0 ],
93
    [ 0, -w + 1, 1, -3*w + 1, w + 2 ],
94
    [ 0, 1, 1, 0, 0 ],
95
    [ 1, w, w + 1, -w + 1, -w ],
96
    [ 1, 1, 0, w - 1, 0 ],
97
    [ 0, w + 1, w, w, -w - 1 ],
98
    [ 0, 0, 1, w - 3, -w + 2 ],
99
    [ w + 1, w + 1, 0, 3*w + 2, 2*w + 1 ],
100
    [ w + 1, -1, w + 1, -2*w - 2, -2*w ],
101
    [ w + 1, w, 0, 2*w - 2, -3*w + 2 ],
102
    [ w, -w + 1, w + 1, -w - 1, 0 ],
103
    [ 1, w, 1, -2, 0 ],
104
    [ 0, -1, w + 1, 0, 0 ],
105
    [ 0, w, 1, -3*w - 2, -3*w - 2 ],
106
    [ 1, -w, w, -w - 1, 0 ],
107
    [ w + 1, w - 1, w + 1, -2*w, -w - 1 ],
108
    [ 0, w + 1, 1, w, w - 2 ],
109
    [ w + 1, w + 1, w, -3, -w + 1 ],
110
    [ 1, -w + 1, w, -w, 0 ],
111
    [ w + 1, -w, 0, -2*w - 1, 0 ],
112
    [ 0, w + 1, w + 1, 0, 0 ],
113
    [ w + 1, -w + 1, w + 1, w + 1, 0 ],
114
    [ 1, w - 1, w + 1, -w, -2 ],
115
    [ w, 0, 0, w - 3, -w + 2 ],
116
    [ w + 1, -w, w, -3*w, 1 ],
117
    [ 1, -w - 1, 0, 2*w, -w ],
118
    [ w, -w + 1, w, -w - 1, -1 ],
119
    [ w, -w, 1, -w + 1, 0 ],
120
    [ w + 1, w - 1, 1, 2*w - 1, 3 ],
121
    [ w + 1, -w - 1, w, -2*w - 2, w + 1 ],
122
    [ 1, w + 1, w, 2*w - 2, -3*w ],
123
    [ 0, -w, w, -2, w + 1 ],
124
    [ 0, 0, w + 1, -2*w + 1, -3 ],
125
    [ w + 1, -w - 1, w + 1, -2*w - 1, 0 ],
126
    [ 1, -w + 1, 1, -3*w - 1, 2*w + 2 ],
127
    [ 1, -w, w + 1, -w - 2, -2*w - 1 ],
128
    [ 0, -w + 1, w, -w + 2, -w + 1 ],
129
    [ 1, -w - 1, 0, -w + 3, -2*w + 3 ],
130
    [ w + 1, -w, w + 1, -3*w - 2, -2*w - 1 ],
131
    [ 1, -1, 1, w - 2, -w + 1 ],
132
    [ w + 1, w + 1, 0, 2*w + 1, -1 ],
133
    [ w, -w + 1, w + 1, -3*w + 1, -w - 1 ],
134
    [ w + 1, 1, 1, -w, 0 ],
135
    [ w, -1, 0, -w, 0 ],
136
    [ w, 1, w, -1, 0 ],
137
    [ w, 0, 1, -3*w - 2, -w - 1 ],
138
    [ w, -w - 1, 1, w + 1, 2*w + 1 ],
139
    [ 1, -1, 0, -3*w - 2, 3*w + 2 ],
140
    [ w, 1, 0, -w, 0 ],
141
    [ 0, w, 1, -w, -w - 1 ],
142
    [ 1, w - 1, 1, -2, -w ],
143
    [ w, 0, 1, -w - 1, 0 ],
144
    [ 0, w + 1, w, -w + 1, -w + 1 ],
145
    [ w, -w, 1, -2*w - 2, 0 ],
146
    [ w, 1, w, -w, -w ],
147
    [ 1, -w + 1, 1, 0, w ],
148
    [ 1, -1, 0, w - 2, -w + 2 ],
149
    [ w, -w + 1, 1, -2*w, 0 ],
150
    [ w, w - 1, 0, 2*w - 3, 0 ],
151
    [ w + 1, 1, w, w - 3, -w + 1 ],
152
    [ w, 1, 0, w - 3, 2*w - 3 ],
153
    [ w, 0, 0, w - 1, 0 ],
154
    [ 1, -w, 1, -2*w - 2, 2*w + 1 ],
155
    [ w + 1, -w + 1, w + 1, -3*w, w - 3 ],
156
    [ w, 1, 0, w, 0 ],
157
    [ w, w - 1, w, -2, -w ],
158
    [ w, 0, 1, w - 3, -w + 2 ],
159
    [ w, -w, w + 1, 3*w + 1, -2*w - 2 ],
160
    [ w + 1, 1, w + 1, w + 1, 0 ],
161
    [ w, -w + 1, 1, -w + 1, -2*w + 3 ],
162
    [ w + 1, w + 1, 1, w + 3, 2*w - 1 ],
163
    [ 1, w - 1, w + 1, -w, -w ],
164
    [ 1, w, 0, 2*w + 1, 0 ],
165
    [ 1, -1, 0, -2*w - 3, 3*w + 3 ],
166
    [ w + 1, -1, 1, 2*w - 3, -w - 3 ],
167
    [ w, -1, w + 1, -2*w - 1, -w - 1 ],
168
    [ 0, -1, w, 2*w - 3, -w + 1 ],
169
    [ w + 1, -1, w + 1, -w - 2, -2*w ],
170
    [ 1, 0, 1, -w, 0 ],
171
    [ w + 1, -w, 0, 2*w - 3, 0 ],
172
    [ w, w - 1, w + 1, -2*w - 1, -2*w - 1 ],
173
    [ w, w + 1, w, -2, -w + 1 ],
174
    [ w, -w, 0, w, 0 ],
175
    [ 1, -w - 1, 1, -1, 0 ],
176
    [ w, w, w, 1, 0 ],
177
    [ w + 1, -w - 1, w, -2*w - 1, 0 ],
178
    [ 1, 0, 0, -w - 1, 0 ],
179
    [ w, 0, 1, -1, 0 ],
180
    [ w, -1, 0, -2*w + 3, 0 ],
181
    [ 0, -w - 1, w, 3*w + 2, -3*w - 2 ],
182
    [ w, w, w, w - 2, -w + 1 ],
183
    [ 0, 1, 1, -w + 2, -2*w + 3 ],
184
    [ w + 1, -1, w, -w - 1, -w + 1 ],
185
    [ 0, -w + 1, w, -2*w, w + 1 ],
186
    [ 1, w, w + 1, 2*w - 1, w + 2 ],
187
    [ w + 1, w + 1, w, w, -w - 1 ],
188
    [ w, -w - 1, 0, -2*w - 1, 0 ],
189
    [ w + 1, w + 1, 1, 2*w, 0 ],
190
    [ w, w + 1, 1, 2*w - 1, 1 ],
191
    [ 1, w, w + 1, -2*w - 1, -3*w - 2 ],
192
    [ w + 1, w - 1, 0, -2*w - 3, 3 ],
193
    [ w, 0, 0, -w + 1, 0 ],
194
    [ w + 1, 0, 0, 1, 2*w - 3 ],
195
    [ 1, 1, 1, w - 1, w - 1 ],
196
    [ 1, -w, w + 1, -3*w - 2, 3*w + 2 ],
197
    [ 0, -1, w + 1, w - 3, -2*w + 3 ],
198
    [ w + 1, 1, 0, -w, 0 ],
199
    [ w, -w - 1, w + 1, -2*w - 2, -w - 1 ],
200
    [ 0, -1, 1, w - 1, w - 2 ],
201
    [ 0, w, w, -1, -w ]
202
    ]
203
    return [EllipticCurve(F, a) for a in v]
204

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206