Isogeny class 36.3-b contains
6 curves linked by isogenies of
degrees dividing 8.
| Curve label |
Weierstrass Coefficients |
| 36.3-b1
| \( \bigl[\frac{1}{2} a^{2} + \frac{1}{2} a - 2\) , \( -\frac{1}{4} a^{3} + \frac{1}{2} a^{2} + \frac{5}{4} a - \frac{3}{2}\) , \( -\frac{1}{4} a^{3} + \frac{11}{4} a + \frac{3}{2}\) , \( \frac{149}{4} a^{3} - 13 a^{2} - \frac{1279}{4} a + \frac{229}{2}\) , \( \frac{201}{4} a^{3} + 8 a^{2} - \frac{1719}{4} a - \frac{133}{2}\bigr] \)
|
| 36.3-b2
| \( \bigl[-\frac{1}{4} a^{3} + \frac{11}{4} a + \frac{3}{2}\) , \( -\frac{1}{4} a^{3} - \frac{1}{2} a^{2} + \frac{13}{4} a + \frac{5}{2}\) , \( -\frac{1}{4} a^{3} + \frac{1}{2} a^{2} + \frac{9}{4} a - \frac{1}{2}\) , \( -\frac{33}{4} a^{3} - 20 a^{2} + \frac{59}{4} a + \frac{33}{2}\) , \( -14 a^{3} - 39 a^{2} + 16 a + 24\bigr] \)
|
| 36.3-b3
| \( \bigl[-\frac{1}{4} a^{3} + \frac{11}{4} a + \frac{1}{2}\) , \( -\frac{1}{4} a^{3} + \frac{1}{2} a^{2} + \frac{9}{4} a - \frac{3}{2}\) , \( a\) , \( -\frac{1}{4} a^{3} + \frac{11}{4} a + \frac{3}{2}\) , \( -\frac{3}{4} a^{3} - \frac{1}{2} a^{2} + \frac{27}{4} a + \frac{9}{2}\bigr] \)
|
| 36.3-b4
| \( \bigl[\frac{1}{4} a^{3} - \frac{7}{4} a - \frac{1}{2}\) , \( \frac{1}{4} a^{3} - \frac{1}{2} a^{2} - \frac{5}{4} a + \frac{3}{2}\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - 1\) , \( -6 a^{3} + \frac{9}{2} a^{2} + \frac{101}{2} a - 37\) , \( \frac{31}{2} a^{3} - \frac{21}{2} a^{2} - 133 a + 91\bigr] \)
|
| 36.3-b5
| \( \bigl[\frac{1}{2} a^{2} + \frac{1}{2} a - 2\) , \( \frac{1}{4} a^{3} - \frac{1}{2} a^{2} - \frac{5}{4} a + \frac{1}{2}\) , \( \frac{1}{4} a^{3} + \frac{1}{2} a^{2} - \frac{9}{4} a - \frac{3}{2}\) , \( -\frac{1}{4} a^{3} + \frac{3}{4} a - \frac{5}{2}\) , \( -a^{2} - 2 a\bigr] \)
|
| 36.3-b6
| \( \bigl[\frac{1}{4} a^{3} - \frac{7}{4} a - \frac{1}{2}\) , \( \frac{1}{4} a^{3} - \frac{1}{2} a^{2} - \frac{5}{4} a + \frac{3}{2}\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - 1\) , \( -\frac{9}{4} a^{3} + 7 a^{2} + \frac{47}{4} a - \frac{79}{2}\) , \( 28 a^{3} - \frac{55}{2} a^{2} - \frac{461}{2} a + 209\bigr] \)
|
Rank: \( 1 \)
\(\left(\begin{array}{rrrrrr}
1 & 2 & 4 & 4 & 8 & 8 \\
2 & 1 & 2 & 2 & 4 & 4 \\
4 & 2 & 1 & 4 & 8 & 8 \\
4 & 2 & 4 & 1 & 2 & 2 \\
8 & 4 & 8 & 2 & 1 & 4 \\
8 & 4 & 8 & 2 & 4 & 1
\end{array}\right)\)
