Isogeny class 16.1-a contains
8 curves linked by isogenies of
degrees dividing 12.
| Curve label |
Weierstrass Coefficients |
| 16.1-a1
| \( \bigl[-\frac{3}{7} a^{3} + \frac{8}{7} a^{2} + \frac{18}{7} a - \frac{29}{7}\) , \( -\frac{3}{7} a^{3} + \frac{8}{7} a^{2} + \frac{18}{7} a - \frac{36}{7}\) , \( -\frac{2}{7} a^{3} + \frac{3}{7} a^{2} + \frac{19}{7} a - \frac{3}{7}\) , \( -2\) , \( -\frac{1}{7} a^{3} - \frac{2}{7} a^{2} + \frac{13}{7} a + \frac{2}{7}\bigr] \)
|
| 16.1-a2
| \( \bigl[-\frac{3}{7} a^{3} + \frac{8}{7} a^{2} + \frac{18}{7} a - \frac{29}{7}\) , \( -\frac{4}{7} a^{3} + \frac{6}{7} a^{2} + \frac{31}{7} a - \frac{27}{7}\) , \( -\frac{2}{7} a^{3} + \frac{3}{7} a^{2} + \frac{19}{7} a - \frac{3}{7}\) , \( 5 a^{3} - 5 a^{2} - 40 a - 7\) , \( \frac{127}{7} a^{3} - \frac{110}{7} a^{2} - \frac{1007}{7} a - \frac{114}{7}\bigr] \)
|
| 16.1-a3
| \( \bigl[-\frac{1}{7} a^{3} + \frac{5}{7} a^{2} - \frac{1}{7} a - \frac{12}{7}\) , \( a + 1\) , \( -\frac{3}{7} a^{3} + \frac{8}{7} a^{2} + \frac{18}{7} a - \frac{29}{7}\) , \( -\frac{40}{7} a^{3} + \frac{81}{7} a^{2} + \frac{282}{7} a - \frac{354}{7}\) , \( \frac{85}{7} a^{3} - \frac{187}{7} a^{2} - \frac{552}{7} a + \frac{726}{7}\bigr] \)
|
| 16.1-a4
| \( \bigl[-\frac{3}{7} a^{3} + \frac{8}{7} a^{2} + \frac{18}{7} a - \frac{29}{7}\) , \( -\frac{3}{7} a^{3} + \frac{8}{7} a^{2} + \frac{18}{7} a - \frac{36}{7}\) , \( -\frac{2}{7} a^{3} + \frac{3}{7} a^{2} + \frac{19}{7} a - \frac{3}{7}\) , \( 5 a^{3} - 5 a^{2} - 40 a - 7\) , \( -\frac{125}{7} a^{3} + \frac{107}{7} a^{2} + \frac{988}{7} a + \frac{110}{7}\bigr] \)
|
| 16.1-a5
| \( \bigl[-\frac{1}{7} a^{3} + \frac{5}{7} a^{2} - \frac{1}{7} a - \frac{12}{7}\) , \( \frac{1}{7} a^{3} - \frac{5}{7} a^{2} + \frac{1}{7} a + \frac{26}{7}\) , \( -\frac{3}{7} a^{3} + \frac{8}{7} a^{2} + \frac{18}{7} a - \frac{29}{7}\) , \( -\frac{38}{7} a^{3} + \frac{71}{7} a^{2} + \frac{270}{7} a - \frac{316}{7}\) , \( -\frac{166}{7} a^{3} + \frac{347}{7} a^{2} + \frac{1115}{7} a - \frac{1439}{7}\bigr] \)
|
| 16.1-a6
| \( \bigl[-\frac{3}{7} a^{3} + \frac{8}{7} a^{2} + \frac{18}{7} a - \frac{29}{7}\) , \( -\frac{4}{7} a^{3} + \frac{6}{7} a^{2} + \frac{31}{7} a - \frac{27}{7}\) , \( -\frac{2}{7} a^{3} + \frac{3}{7} a^{2} + \frac{19}{7} a - \frac{3}{7}\) , \( -2\) , \( \frac{3}{7} a^{3} - \frac{1}{7} a^{2} - \frac{32}{7} a - \frac{6}{7}\bigr] \)
|
| 16.1-a7
| \( \bigl[0\) , \( \frac{1}{7} a^{3} + \frac{2}{7} a^{2} - \frac{13}{7} a - \frac{9}{7}\) , \( 0\) , \( -\frac{2}{7} a^{3} + \frac{3}{7} a^{2} + \frac{12}{7} a + \frac{4}{7}\) , \( \frac{32}{7} a^{3} - \frac{27}{7} a^{2} - \frac{255}{7} a - \frac{29}{7}\bigr] \)
|
| 16.1-a8
| \( \bigl[0\) , \( \frac{1}{7} a^{3} - \frac{5}{7} a^{2} - \frac{6}{7} a + \frac{19}{7}\) , \( 0\) , \( \frac{2}{7} a^{3} - \frac{3}{7} a^{2} - \frac{12}{7} a + \frac{17}{7}\) , \( \frac{32}{7} a^{3} - \frac{69}{7} a^{2} - \frac{213}{7} a + \frac{279}{7}\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrrrrrr}
1 & 6 & 2 & 2 & 6 & 3 & 6 & 2 \\
6 & 1 & 3 & 12 & 4 & 2 & 4 & 12 \\
2 & 3 & 1 & 4 & 12 & 6 & 12 & 4 \\
2 & 12 & 4 & 1 & 3 & 6 & 12 & 4 \\
6 & 4 & 12 & 3 & 1 & 2 & 4 & 12 \\
3 & 2 & 6 & 6 & 2 & 1 & 2 & 6 \\
6 & 4 & 12 & 12 & 4 & 2 & 1 & 3 \\
2 & 12 & 4 & 4 & 12 & 6 & 3 & 1
\end{array}\right)\)
