Isogeny class 36.2-a contains
4 curves linked by isogenies of
degrees dividing 6.
Curve label |
Weierstrass Coefficients |
36.2-a1
| \( \bigl[\frac{1}{4} a^{3} + \frac{1}{2} a^{2} - \frac{9}{4} a - \frac{5}{2}\) , \( \frac{1}{4} a^{3} + \frac{1}{2} a^{2} - \frac{9}{4} a - \frac{3}{2}\) , \( \frac{1}{4} a^{3} + \frac{1}{2} a^{2} - \frac{9}{4} a - \frac{5}{2}\) , \( \frac{3}{4} a^{3} + \frac{3}{2} a^{2} - \frac{23}{4} a - \frac{15}{2}\) , \( \frac{1}{4} a^{3} - \frac{11}{4} a - \frac{1}{2}\bigr] \)
|
36.2-a2
| \( \bigl[-\frac{1}{4} a^{3} + \frac{11}{4} a + \frac{3}{2}\) , \( \frac{1}{4} a^{3} - \frac{1}{2} a^{2} - \frac{9}{4} a + \frac{5}{2}\) , \( -\frac{1}{4} a^{3} + \frac{11}{4} a + \frac{1}{2}\) , \( -\frac{3}{4} a^{3} + 2 a^{2} - \frac{11}{4} a + \frac{3}{2}\) , \( -\frac{3}{4} a^{3} + \frac{5}{2} a^{2} - \frac{1}{4} a - \frac{1}{2}\bigr] \)
|
36.2-a3
| \( \bigl[1\) , \( \frac{1}{4} a^{3} - \frac{1}{2} a^{2} - \frac{9}{4} a + \frac{5}{2}\) , \( a\) , \( a^{3} - \frac{5}{2} a^{2} - \frac{9}{2} a + 4\) , \( -\frac{3}{2} a^{3} + \frac{9}{2} a^{2} - a - 1\bigr] \)
|
36.2-a4
| \( \bigl[\frac{1}{4} a^{3} - \frac{7}{4} a + \frac{1}{2}\) , \( -\frac{1}{4} a^{3} - \frac{1}{2} a^{2} + \frac{13}{4} a + \frac{3}{2}\) , \( -\frac{1}{4} a^{3} + \frac{11}{4} a + \frac{1}{2}\) , \( \frac{11}{2} a^{3} + \frac{9}{2} a^{2} - 49 a - 34\) , \( -\frac{25}{2} a^{3} - 9 a^{2} + \frac{215}{2} a + 73\bigr] \)
|
Rank: \( 1 \)
\(\left(\begin{array}{rrrr}
1 & 6 & 2 & 3 \\
6 & 1 & 3 & 2 \\
2 & 3 & 1 & 6 \\
3 & 2 & 6 & 1
\end{array}\right)\)