Isogeny class 625.1-c contains
12 curves linked by isogenies of
degrees dividing 90.
| Curve label |
Weierstrass Coefficients |
| 625.1-c1
| \( \bigl[-\frac{3}{7} a^{3} + \frac{8}{7} a^{2} + \frac{18}{7} a - \frac{29}{7}\) , \( -\frac{1}{7} a^{3} - \frac{2}{7} a^{2} + \frac{13}{7} a + \frac{16}{7}\) , \( -\frac{2}{7} a^{3} + \frac{3}{7} a^{2} + \frac{19}{7} a - \frac{10}{7}\) , \( -\frac{997}{7} a^{3} + \frac{1275}{7} a^{2} + \frac{7578}{7} a - \frac{2248}{7}\) , \( -1737 a^{3} + 1194 a^{2} + 14215 a + 4288\bigr] \)
|
| 625.1-c2
| \( \bigl[-\frac{3}{7} a^{3} + \frac{8}{7} a^{2} + \frac{18}{7} a - \frac{29}{7}\) , \( \frac{1}{7} a^{3} - \frac{5}{7} a^{2} + \frac{1}{7} a + \frac{19}{7}\) , \( -\frac{2}{7} a^{3} + \frac{3}{7} a^{2} + \frac{19}{7} a - \frac{10}{7}\) , \( -\frac{201}{7} a^{3} + \frac{508}{7} a^{2} - \frac{404}{7} a + \frac{24}{7}\) , \( \frac{2398}{7} a^{3} - \frac{13852}{7} a^{2} + \frac{10987}{7} a + \frac{1448}{7}\bigr] \)
|
| 625.1-c3
| \( \bigl[-\frac{3}{7} a^{3} + \frac{8}{7} a^{2} + \frac{18}{7} a - \frac{29}{7}\) , \( \frac{1}{7} a^{3} - \frac{5}{7} a^{2} + \frac{1}{7} a + \frac{19}{7}\) , \( -\frac{2}{7} a^{3} + \frac{3}{7} a^{2} + \frac{19}{7} a - \frac{10}{7}\) , \( \frac{24}{7} a^{3} - \frac{92}{7} a^{2} - \frac{4}{7} a + \frac{99}{7}\) , \( -\frac{142}{7} a^{3} + \frac{633}{7} a^{2} - \frac{548}{7} a + \frac{18}{7}\bigr] \)
|
| 625.1-c4
| \( \bigl[-\frac{3}{7} a^{3} + \frac{8}{7} a^{2} + \frac{18}{7} a - \frac{29}{7}\) , \( \frac{1}{7} a^{3} - \frac{5}{7} a^{2} - \frac{6}{7} a + \frac{26}{7}\) , \( -\frac{3}{7} a^{3} + \frac{8}{7} a^{2} + \frac{18}{7} a - \frac{22}{7}\) , \( -\frac{198}{7} a^{3} + \frac{500}{7} a^{2} - \frac{415}{7} a + \frac{39}{7}\) , \( -\frac{2262}{7} a^{3} + \frac{13403}{7} a^{2} - \frac{10872}{7} a - \frac{1335}{7}\bigr] \)
|
| 625.1-c5
| \( \bigl[-\frac{3}{7} a^{3} + \frac{8}{7} a^{2} + \frac{18}{7} a - \frac{29}{7}\) , \( \frac{3}{7} a^{3} - \frac{8}{7} a^{2} - \frac{18}{7} a + \frac{29}{7}\) , \( -\frac{3}{7} a^{3} + \frac{8}{7} a^{2} + \frac{18}{7} a - \frac{22}{7}\) , \( -\frac{986}{7} a^{3} + \frac{1255}{7} a^{2} + \frac{7505}{7} a - \frac{2193}{7}\) , \( \frac{9402}{7} a^{3} - \frac{3722}{7} a^{2} - \frac{79687}{7} a - \frac{44788}{7}\bigr] \)
|
| 625.1-c6
| \( \bigl[-\frac{3}{7} a^{3} + \frac{8}{7} a^{2} + \frac{18}{7} a - \frac{29}{7}\) , \( \frac{1}{7} a^{3} - \frac{5}{7} a^{2} - \frac{6}{7} a + \frac{26}{7}\) , \( -\frac{3}{7} a^{3} + \frac{8}{7} a^{2} + \frac{18}{7} a - \frac{22}{7}\) , \( \frac{27}{7} a^{3} - \frac{100}{7} a^{2} - \frac{15}{7} a + \frac{114}{7}\) , \( \frac{153}{7} a^{3} - \frac{632}{7} a^{2} + \frac{363}{7} a + \frac{170}{7}\bigr] \)
|
| 625.1-c7
| \( \bigl[-\frac{1}{7} a^{3} + \frac{5}{7} a^{2} - \frac{1}{7} a - \frac{12}{7}\) , \( -\frac{3}{7} a^{3} + \frac{8}{7} a^{2} + \frac{18}{7} a - \frac{22}{7}\) , \( -\frac{2}{7} a^{3} + \frac{3}{7} a^{2} + \frac{19}{7} a - \frac{10}{7}\) , \( \frac{998}{7} a^{3} - \frac{1700}{7} a^{2} - \frac{7192}{7} a + \frac{5571}{7}\) , \( -\frac{11038}{7} a^{3} + \frac{26812}{7} a^{2} + \frac{71093}{7} a - \frac{124259}{7}\bigr] \)
|
| 625.1-c8
| \( \bigl[-\frac{1}{7} a^{3} + \frac{5}{7} a^{2} - \frac{1}{7} a - \frac{12}{7}\) , \( -\frac{1}{7} a^{3} + \frac{5}{7} a^{2} - \frac{1}{7} a - \frac{12}{7}\) , \( -\frac{1}{7} a^{3} + \frac{5}{7} a^{2} - \frac{1}{7} a - \frac{19}{7}\) , \( \frac{206}{7} a^{3} - \frac{85}{7} a^{2} - \frac{95}{7} a - \frac{111}{7}\) , \( -\frac{2034}{7} a^{3} - \frac{7330}{7} a^{2} + \frac{9691}{7} a + \frac{1093}{7}\bigr] \)
|
| 625.1-c9
| \( \bigl[-\frac{1}{7} a^{3} + \frac{5}{7} a^{2} - \frac{1}{7} a - \frac{12}{7}\) , \( -\frac{1}{7} a^{3} + \frac{5}{7} a^{2} + \frac{6}{7} a - \frac{12}{7}\) , \( -\frac{2}{7} a^{3} + \frac{3}{7} a^{2} + \frac{19}{7} a - \frac{10}{7}\) , \( \frac{206}{7} a^{3} - \frac{85}{7} a^{2} - \frac{88}{7} a - \frac{104}{7}\) , \( \frac{2633}{7} a^{3} + \frac{5931}{7} a^{2} - \frac{9008}{7} a - \frac{954}{7}\bigr] \)
|
| 625.1-c10
| \( \bigl[-\frac{1}{7} a^{3} + \frac{5}{7} a^{2} - \frac{1}{7} a - \frac{12}{7}\) , \( -\frac{3}{7} a^{3} + \frac{8}{7} a^{2} + \frac{18}{7} a - \frac{22}{7}\) , \( -\frac{2}{7} a^{3} + \frac{3}{7} a^{2} + \frac{19}{7} a - \frac{10}{7}\) , \( -11 a^{3} + 25 a^{2} + 69 a - 97\) , \( \frac{702}{7} a^{3} - \frac{1473}{7} a^{2} - \frac{4772}{7} a + \frac{6121}{7}\bigr] \)
|
| 625.1-c11
| \( \bigl[-\frac{1}{7} a^{3} + \frac{5}{7} a^{2} - \frac{1}{7} a - \frac{12}{7}\) , \( -\frac{1}{7} a^{3} + \frac{5}{7} a^{2} - \frac{1}{7} a - \frac{12}{7}\) , \( -\frac{1}{7} a^{3} + \frac{5}{7} a^{2} - \frac{1}{7} a - \frac{19}{7}\) , \( -\frac{19}{7} a^{3} - \frac{10}{7} a^{2} + \frac{30}{7} a - \frac{11}{7}\) , \( \frac{131}{7} a^{3} + \frac{185}{7} a^{2} - \frac{324}{7} a - \frac{52}{7}\bigr] \)
|
| 625.1-c12
| \( \bigl[-\frac{1}{7} a^{3} + \frac{5}{7} a^{2} - \frac{1}{7} a - \frac{12}{7}\) , \( \frac{1}{7} a^{3} + \frac{2}{7} a^{2} - \frac{13}{7} a - \frac{2}{7}\) , \( -\frac{1}{7} a^{3} + \frac{5}{7} a^{2} - \frac{1}{7} a - \frac{19}{7}\) , \( \frac{998}{7} a^{3} - \frac{1700}{7} a^{2} - \frac{7185}{7} a + \frac{5550}{7}\) , \( \frac{10510}{7} a^{3} - \frac{25775}{7} a^{2} - \frac{67484}{7} a + \frac{120254}{7}\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrrrrrrrrrr}
1 & 9 & 3 & 5 & 45 & 15 & 18 & 90 & 2 & 6 & 30 & 10 \\
9 & 1 & 3 & 45 & 5 & 15 & 2 & 10 & 18 & 6 & 30 & 90 \\
3 & 3 & 1 & 15 & 15 & 5 & 6 & 30 & 6 & 2 & 10 & 30 \\
5 & 45 & 15 & 1 & 9 & 3 & 90 & 18 & 10 & 30 & 6 & 2 \\
45 & 5 & 15 & 9 & 1 & 3 & 10 & 2 & 90 & 30 & 6 & 18 \\
15 & 15 & 5 & 3 & 3 & 1 & 30 & 6 & 30 & 10 & 2 & 6 \\
18 & 2 & 6 & 90 & 10 & 30 & 1 & 5 & 9 & 3 & 15 & 45 \\
90 & 10 & 30 & 18 & 2 & 6 & 5 & 1 & 45 & 15 & 3 & 9 \\
2 & 18 & 6 & 10 & 90 & 30 & 9 & 45 & 1 & 3 & 15 & 5 \\
6 & 6 & 2 & 30 & 30 & 10 & 3 & 15 & 3 & 1 & 5 & 15 \\
30 & 30 & 10 & 6 & 6 & 2 & 15 & 3 & 15 & 5 & 1 & 3 \\
10 & 90 & 30 & 2 & 18 & 6 & 45 & 9 & 5 & 15 & 3 & 1
\end{array}\right)\)
