Isogeny class 29.3-e contains
6 curves linked by isogenies of
degrees dividing 8.
| Curve label |
Weierstrass Coefficients |
| 29.3-e1
| \( \bigl[-\frac{1}{4} a^{3} + \frac{1}{2} a^{2} + \frac{9}{4} a - \frac{1}{2}\) , \( \frac{1}{4} a^{3} - \frac{11}{4} a - \frac{1}{2}\) , \( \frac{1}{4} a^{3} - \frac{7}{4} a - \frac{1}{2}\) , \( -\frac{7}{2} a^{2} + \frac{13}{2} a + 4\) , \( \frac{99}{2} a^{3} - 145 a^{2} - \frac{51}{2} a + 67\bigr] \)
|
| 29.3-e2
| \( \bigl[-\frac{1}{4} a^{3} + \frac{11}{4} a + \frac{3}{2}\) , \( -\frac{1}{4} a^{3} - \frac{1}{2} a^{2} + \frac{13}{4} a + \frac{7}{2}\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - 1\) , \( -\frac{9}{2} a^{3} + a^{2} + \frac{77}{2} a - 3\) , \( \frac{99}{4} a^{3} - 19 a^{2} - \frac{837}{4} a + \frac{321}{2}\bigr] \)
|
| 29.3-e3
| \( \bigl[\frac{1}{2} a^{2} - \frac{1}{2} a - 2\) , \( 0\) , \( a + 1\) , \( -\frac{3}{2} a^{2} + \frac{5}{2} a + 1\) , \( \frac{7}{4} a^{3} - \frac{11}{2} a^{2} - \frac{7}{4} a + \frac{5}{2}\bigr] \)
|
| 29.3-e4
| \( \bigl[\frac{1}{2} a^{2} + \frac{1}{2} a - 2\) , \( -\frac{1}{2} a^{2} - \frac{1}{2} a + 1\) , \( a + 1\) , \( -\frac{95}{4} a^{3} + \frac{31}{2} a^{2} + \frac{807}{4} a - \frac{273}{2}\) , \( -\frac{103}{4} a^{3} + \frac{35}{2} a^{2} + \frac{875}{4} a - \frac{301}{2}\bigr] \)
|
| 29.3-e5
| \( \bigl[1\) , \( -\frac{1}{4} a^{3} - \frac{1}{2} a^{2} + \frac{13}{4} a + \frac{7}{2}\) , \( -\frac{1}{4} a^{3} + \frac{1}{2} a^{2} + \frac{9}{4} a - \frac{1}{2}\) , \( \frac{5}{2} a^{3} + 2 a^{2} - \frac{43}{2} a - 17\) , \( \frac{361}{2} a^{3} + 124 a^{2} - \frac{3081}{2} a - 1060\bigr] \)
|
| 29.3-e6
| \( \bigl[\frac{1}{4} a^{3} - \frac{7}{4} a + \frac{1}{2}\) , \( -\frac{1}{2} a^{3} - \frac{1}{2} a^{2} + 5 a + 3\) , \( \frac{1}{4} a^{3} + \frac{1}{2} a^{2} - \frac{9}{4} a - \frac{3}{2}\) , \( -\frac{1}{2} a^{3} + \frac{1}{2} a^{2} + 5 a + 3\) , \( \frac{1}{4} a^{3} - \frac{3}{2} a^{2} - \frac{25}{4} a - \frac{7}{2}\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrrrr}
1 & 4 & 2 & 4 & 8 & 8 \\
4 & 1 & 2 & 4 & 8 & 8 \\
2 & 2 & 1 & 2 & 4 & 4 \\
4 & 4 & 2 & 1 & 2 & 2 \\
8 & 8 & 4 & 2 & 1 & 4 \\
8 & 8 & 4 & 2 & 4 & 1
\end{array}\right)\)
