Isogeny class 9.1-a contains
8 curves linked by isogenies of
degrees dividing 16.
| Curve label |
Weierstrass Coefficients |
| 9.1-a1
| \( \bigl[1\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - 3\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - 1\) , \( -\frac{883}{2} a^{3} + 299 a^{2} + \frac{7557}{2} a - 2587\) , \( -\frac{46471}{4} a^{3} + 7963 a^{2} + \frac{396341}{4} a - \frac{135709}{2}\bigr] \)
|
| 9.1-a2
| \( \bigl[\frac{1}{4} a^{3} - \frac{7}{4} a - \frac{1}{2}\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 4 a + 1\) , \( -\frac{1}{4} a^{3} + \frac{11}{4} a + \frac{3}{2}\) , \( -\frac{3}{4} a^{3} + \frac{3}{2} a^{2} + \frac{7}{4} a + \frac{3}{2}\) , \( 6 a^{3} - 17 a^{2} - 5 a + 7\bigr] \)
|
| 9.1-a3
| \( \bigl[\frac{1}{2} a^{2} + \frac{1}{2} a - 2\) , \( -a - 1\) , \( 0\) , \( -a^{3} + 7 a + 6\) , \( \frac{3}{4} a^{3} + 2 a^{2} - \frac{41}{4} a - \frac{13}{2}\bigr] \)
|
| 9.1-a4
| \( \bigl[\frac{1}{2} a^{2} + \frac{1}{2} a - 2\) , \( -a - 1\) , \( 0\) , \( \frac{1}{4} a^{3} - \frac{7}{4} a - \frac{3}{2}\) , \( 0\bigr] \)
|
| 9.1-a5
| \( \bigl[1\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - 3\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - 1\) , \( -\frac{111}{4} a^{3} + 19 a^{2} + \frac{949}{4} a - \frac{329}{2}\) , \( -\frac{319}{2} a^{3} + 109 a^{2} + \frac{2723}{2} a - 933\bigr] \)
|
| 9.1-a6
| \( \bigl[-\frac{1}{4} a^{3} + \frac{11}{4} a + \frac{3}{2}\) , \( \frac{1}{4} a^{3} - \frac{1}{2} a^{2} - \frac{9}{4} a + \frac{3}{2}\) , \( \frac{1}{4} a^{3} + \frac{1}{2} a^{2} - \frac{9}{4} a - \frac{3}{2}\) , \( -\frac{55}{4} a^{3} - 40 a^{2} + \frac{33}{4} a + \frac{45}{2}\) , \( -\frac{513}{4} a^{3} - \frac{751}{2} a^{2} + \frac{233}{4} a + \frac{351}{2}\bigr] \)
|
| 9.1-a7
| \( \bigl[\frac{1}{4} a^{3} - \frac{7}{4} a + \frac{1}{2}\) , \( -\frac{1}{4} a^{3} + \frac{1}{2} a^{2} + \frac{5}{4} a - \frac{1}{2}\) , \( a\) , \( 2 a^{3} - a^{2} - 19 a + 13\) , \( -\frac{45}{2} a^{3} + \frac{31}{2} a^{2} + 191 a - 131\bigr] \)
|
| 9.1-a8
| \( \bigl[-\frac{1}{4} a^{3} + \frac{11}{4} a + \frac{3}{2}\) , \( \frac{1}{4} a^{3} - \frac{1}{2} a^{2} - \frac{9}{4} a + \frac{3}{2}\) , \( \frac{1}{4} a^{3} + \frac{1}{2} a^{2} - \frac{9}{4} a - \frac{3}{2}\) , \( -\frac{35}{4} a^{3} - 35 a^{2} - \frac{47}{4} a + \frac{15}{2}\) , \( -\frac{679}{4} a^{3} - 499 a^{2} + \frac{401}{4} a + \frac{497}{2}\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrrrrrr}
1 & 16 & 8 & 4 & 2 & 8 & 4 & 16 \\
16 & 1 & 8 & 4 & 8 & 2 & 16 & 4 \\
8 & 8 & 1 & 2 & 4 & 4 & 8 & 8 \\
4 & 4 & 2 & 1 & 2 & 2 & 4 & 4 \\
2 & 8 & 4 & 2 & 1 & 4 & 2 & 8 \\
8 & 2 & 4 & 2 & 4 & 1 & 8 & 2 \\
4 & 16 & 8 & 4 & 2 & 8 & 1 & 16 \\
16 & 4 & 8 & 4 & 8 & 2 & 16 & 1
\end{array}\right)\)
