Isogeny class 36.4-a contains
4 curves linked by isogenies of
degrees dividing 6.
| Curve label |
Weierstrass Coefficients |
| 36.4-a1
| \( \bigl[\frac{1}{4} a^{3} - \frac{7}{4} a - \frac{1}{2}\) , \( \frac{1}{4} a^{3} + \frac{1}{2} a^{2} - \frac{13}{4} a - \frac{3}{2}\) , \( -\frac{1}{4} a^{3} + \frac{1}{2} a^{2} + \frac{9}{4} a - \frac{3}{2}\) , \( -2 a^{3} - \frac{7}{2} a^{2} + \frac{5}{2} a + 3\) , \( \frac{9}{2} a^{3} + \frac{29}{2} a^{2} - a - 8\bigr] \)
|
| 36.4-a2
| \( \bigl[1\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - 2\) , \( a + 1\) , \( -\frac{5}{2} a^{3} + \frac{5}{2} a^{2} + 20 a - 19\) , \( \frac{29}{4} a^{3} - 5 a^{2} - \frac{251}{4} a + \frac{83}{2}\bigr] \)
|
| 36.4-a3
| \( \bigl[-\frac{1}{4} a^{3} + \frac{11}{4} a + \frac{3}{2}\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - 2\) , \( -\frac{1}{4} a^{3} + \frac{11}{4} a + \frac{1}{2}\) , \( \frac{19}{4} a^{3} - 2 a^{2} - \frac{165}{4} a + \frac{39}{2}\) , \( \frac{7}{2} a^{3} - \frac{5}{2} a^{2} - 30 a + 22\bigr] \)
|
| 36.4-a4
| \( \bigl[\frac{1}{2} a^{2} + \frac{1}{2} a - 2\) , \( -\frac{1}{2} a^{2} - \frac{1}{2} a + 3\) , \( \frac{1}{2} a^{2} + \frac{1}{2} a - 2\) , \( -\frac{1}{2} a^{3} - \frac{3}{2} a^{2} + 3 a + 6\) , \( \frac{1}{4} a^{3} - \frac{11}{4} a - \frac{1}{2}\bigr] \)
|
Rank: \( 1 \)
\(\left(\begin{array}{rrrr}
1 & 6 & 2 & 3 \\
6 & 1 & 3 & 2 \\
2 & 3 & 1 & 6 \\
3 & 2 & 6 & 1
\end{array}\right)\)
