Isogeny class 29.1-e contains
6 curves linked by isogenies of
degrees dividing 8.
| Curve label |
Weierstrass Coefficients |
| 29.1-e1
| \( \bigl[\frac{1}{4} a^{3} + \frac{1}{2} a^{2} - \frac{9}{4} a - \frac{5}{2}\) , \( -\frac{1}{2} a^{2} + \frac{3}{2} a + 3\) , \( \frac{1}{2} a^{2} + \frac{1}{2} a - 1\) , \( \frac{7}{2} a^{3} - \frac{7}{2} a^{2} - 33 a + 40\) , \( \frac{15}{2} a^{3} - \frac{17}{2} a^{2} - 60 a + 57\bigr] \)
|
| 29.1-e2
| \( \bigl[\frac{1}{4} a^{3} - \frac{7}{4} a - \frac{1}{2}\) , \( a + 1\) , \( \frac{1}{4} a^{3} + \frac{1}{2} a^{2} - \frac{9}{4} a - \frac{3}{2}\) , \( -\frac{1}{4} a^{3} - a^{2} - \frac{5}{4} a - \frac{1}{2}\) , \( -\frac{5}{4} a^{3} - \frac{9}{2} a^{2} - \frac{7}{4} a + \frac{1}{2}\bigr] \)
|
| 29.1-e3
| \( \bigl[1\) , \( \frac{1}{4} a^{3} + \frac{1}{2} a^{2} - \frac{13}{4} a - \frac{5}{2}\) , \( -\frac{1}{4} a^{3} + \frac{1}{2} a^{2} + \frac{9}{4} a - \frac{3}{2}\) , \( -\frac{3}{2} a^{3} - \frac{5}{2} a^{2} + 5 a + 3\) , \( -\frac{81}{2} a^{3} - 119 a^{2} + \frac{37}{2} a + 55\bigr] \)
|
| 29.1-e4
| \( \bigl[-\frac{1}{4} a^{3} + \frac{1}{2} a^{2} + \frac{9}{4} a - \frac{1}{2}\) , \( \frac{1}{4} a^{3} - \frac{1}{2} a^{2} - \frac{9}{4} a + \frac{3}{2}\) , \( a\) , \( -2 a^{3} + \frac{3}{2} a^{2} + \frac{31}{2} a - 14\) , \( -\frac{29}{4} a^{3} + 5 a^{2} + \frac{247}{4} a - \frac{89}{2}\bigr] \)
|
| 29.1-e5
| \( \bigl[-\frac{1}{4} a^{3} + \frac{11}{4} a + \frac{3}{2}\) , \( \frac{1}{4} a^{3} + \frac{1}{2} a^{2} - \frac{13}{4} a - \frac{5}{2}\) , \( -\frac{1}{4} a^{3} + \frac{1}{2} a^{2} + \frac{9}{4} a - \frac{1}{2}\) , \( \frac{1}{4} a^{3} - \frac{3}{2} a^{2} - \frac{1}{4} a - \frac{1}{2}\) , \( -\frac{11}{2} a^{3} + \frac{31}{2} a^{2} + 3 a - 8\bigr] \)
|
| 29.1-e6
| \( \bigl[\frac{1}{2} a^{2} - \frac{1}{2} a - 2\) , \( \frac{1}{4} a^{3} - \frac{1}{2} a^{2} - \frac{9}{4} a + \frac{5}{2}\) , \( \frac{1}{4} a^{3} - \frac{7}{4} a + \frac{1}{2}\) , \( -\frac{7}{2} a^{3} + \frac{7}{2} a^{2} + 31 a - 28\) , \( -210 a^{3} + 145 a^{2} + 1791 a - 1238\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrrrr}
1 & 2 & 4 & 4 & 8 & 8 \\
2 & 1 & 2 & 2 & 4 & 4 \\
4 & 2 & 1 & 4 & 8 & 8 \\
4 & 2 & 4 & 1 & 2 & 2 \\
8 & 4 & 8 & 2 & 1 & 4 \\
8 & 4 & 8 & 2 & 4 & 1
\end{array}\right)\)
