Isogeny class 1.1-a contains
12 curves linked by isogenies of
degrees dividing 24.
| Curve label |
Weierstrass Coefficients |
| 1.1-a1
| \( \bigl[\frac{1}{4} a^{3} + \frac{1}{2} a^{2} - \frac{9}{4} a - \frac{5}{2}\) , \( -\frac{1}{4} a^{3} + \frac{11}{4} a - \frac{1}{2}\) , \( \frac{1}{4} a^{3} - \frac{7}{4} a - \frac{1}{2}\) , \( -\frac{11}{4} a^{3} + \frac{3}{2} a^{2} + \frac{95}{4} a - \frac{25}{2}\) , \( -\frac{19}{4} a^{3} + 5 a^{2} + \frac{129}{4} a - \frac{43}{2}\bigr] \)
|
| 1.1-a2
| \( \bigl[\frac{1}{4} a^{3} + \frac{1}{2} a^{2} - \frac{9}{4} a - \frac{5}{2}\) , \( -\frac{1}{4} a^{3} + \frac{11}{4} a - \frac{1}{2}\) , \( \frac{1}{4} a^{3} - \frac{7}{4} a - \frac{1}{2}\) , \( -\frac{1}{4} a^{3} - a^{2} + \frac{15}{4} a + \frac{5}{2}\) , \( -\frac{3}{4} a^{3} + a^{2} + \frac{9}{4} a + \frac{3}{2}\bigr] \)
|
| 1.1-a3
| \( \bigl[\frac{1}{2} a^{2} - \frac{1}{2} a - 2\) , \( \frac{1}{4} a^{3} - \frac{11}{4} a - \frac{1}{2}\) , \( \frac{1}{4} a^{3} - \frac{7}{4} a - \frac{1}{2}\) , \( a^{3} + \frac{3}{2} a^{2} - \frac{21}{2} a - 8\) , \( -\frac{9}{4} a^{3} - a^{2} + \frac{75}{4} a + \frac{21}{2}\bigr] \)
|
| 1.1-a4
| \( \bigl[\frac{1}{2} a^{2} - \frac{1}{2} a - 2\) , \( \frac{1}{4} a^{3} - \frac{11}{4} a - \frac{1}{2}\) , \( \frac{1}{4} a^{3} - \frac{7}{4} a - \frac{1}{2}\) , \( -\frac{1}{4} a^{3} - a^{2} - \frac{17}{4} a - \frac{1}{2}\) , \( -\frac{21}{4} a^{3} - 5 a^{2} + \frac{151}{4} a + \frac{47}{2}\bigr] \)
|
| 1.1-a5
| \( \bigl[\frac{1}{2} a^{2} + \frac{1}{2} a - 2\) , \( -\frac{1}{4} a^{3} + \frac{11}{4} a - \frac{1}{2}\) , \( \frac{1}{4} a^{3} - \frac{7}{4} a + \frac{1}{2}\) , \( -\frac{3}{4} a^{3} + a^{2} + \frac{29}{4} a - \frac{13}{2}\) , \( \frac{9}{4} a^{3} - a^{2} - \frac{75}{4} a + \frac{21}{2}\bigr] \)
|
| 1.1-a6
| \( \bigl[\frac{1}{2} a^{2} + \frac{1}{2} a - 2\) , \( -\frac{1}{4} a^{3} + \frac{11}{4} a - \frac{1}{2}\) , \( \frac{1}{4} a^{3} - \frac{7}{4} a + \frac{1}{2}\) , \( \frac{1}{2} a^{3} - \frac{3}{2} a^{2} + a + 1\) , \( \frac{21}{4} a^{3} - 5 a^{2} - \frac{151}{4} a + \frac{47}{2}\bigr] \)
|
| 1.1-a7
| \( \bigl[-\frac{1}{4} a^{3} + \frac{1}{2} a^{2} + \frac{9}{4} a - \frac{1}{2}\) , \( -\frac{1}{4} a^{3} - \frac{1}{2} a^{2} + \frac{13}{4} a + \frac{5}{2}\) , \( 0\) , \( 2 a^{3} + 2 a^{2} - 16 a - 12\) , \( \frac{41}{4} a^{3} + 9 a^{2} - \frac{315}{4} a - \frac{111}{2}\bigr] \)
|
| 1.1-a8
| \( \bigl[-\frac{1}{4} a^{3} + \frac{1}{2} a^{2} + \frac{9}{4} a - \frac{1}{2}\) , \( -\frac{1}{4} a^{3} - \frac{1}{2} a^{2} + \frac{13}{4} a + \frac{5}{2}\) , \( 0\) , \( -\frac{1}{2} a^{3} - \frac{1}{2} a^{2} + 4 a + 3\) , \( 0\bigr] \)
|
| 1.1-a9
| \( \bigl[-\frac{1}{4} a^{3} + \frac{11}{4} a + \frac{1}{2}\) , \( \frac{1}{4} a^{3} - \frac{11}{4} a + \frac{1}{2}\) , \( a\) , \( -\frac{1}{2} a^{3} + \frac{7}{2} a - 2\) , \( -a^{3} + \frac{1}{2} a^{2} + \frac{17}{2} a - 6\bigr] \)
|
| 1.1-a10
| \( \bigl[-\frac{1}{4} a^{3} + \frac{11}{4} a + \frac{1}{2}\) , \( \frac{1}{4} a^{3} - \frac{11}{4} a + \frac{1}{2}\) , \( a + 1\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 4 a\) , \( \frac{1}{4} a^{3} - a^{2} - \frac{3}{4} a + \frac{1}{2}\bigr] \)
|
| 1.1-a11
| \( \bigl[-\frac{1}{4} a^{3} + \frac{11}{4} a + \frac{3}{2}\) , \( 0\) , \( a\) , \( \frac{1}{2} a^{3} - \frac{9}{2} a - 2\) , \( a^{3} + \frac{1}{2} a^{2} - \frac{17}{2} a - 6\bigr] \)
|
| 1.1-a12
| \( \bigl[-\frac{1}{4} a^{3} + \frac{11}{4} a + \frac{3}{2}\) , \( 0\) , \( a + 1\) , \( -\frac{1}{4} a^{3} - \frac{1}{2} a^{2} + \frac{1}{4} a - \frac{1}{2}\) , \( -\frac{1}{4} a^{3} - a^{2} - \frac{1}{4} a + \frac{1}{2}\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrrrrrrrrrr}
1 & 2 & 12 & 24 & 4 & 8 & 3 & 6 & 12 & 24 & 4 & 8 \\
2 & 1 & 6 & 12 & 2 & 4 & 6 & 3 & 6 & 12 & 2 & 4 \\
12 & 6 & 1 & 2 & 3 & 6 & 4 & 2 & 4 & 2 & 12 & 6 \\
24 & 12 & 2 & 1 & 6 & 3 & 8 & 4 & 8 & 4 & 24 & 12 \\
4 & 2 & 3 & 6 & 1 & 2 & 12 & 6 & 12 & 6 & 4 & 2 \\
8 & 4 & 6 & 3 & 2 & 1 & 24 & 12 & 24 & 12 & 8 & 4 \\
3 & 6 & 4 & 8 & 12 & 24 & 1 & 2 & 4 & 8 & 12 & 24 \\
6 & 3 & 2 & 4 & 6 & 12 & 2 & 1 & 2 & 4 & 6 & 12 \\
12 & 6 & 4 & 8 & 12 & 24 & 4 & 2 & 1 & 8 & 3 & 24 \\
24 & 12 & 2 & 4 & 6 & 12 & 8 & 4 & 8 & 1 & 24 & 3 \\
4 & 2 & 12 & 24 & 4 & 8 & 12 & 6 & 3 & 24 & 1 & 8 \\
8 & 4 & 6 & 12 & 2 & 4 & 24 & 12 & 24 & 3 & 8 & 1
\end{array}\right)\)
