Elliptic curves in class 8.1-a over 4.4.13968.1
Isogeny class 8.1-a contains
4 curves linked by isogenies of
degrees dividing 6.
| Curve label |
Weierstrass Coefficients |
| 8.1-a1
| \( \bigl[\frac{1}{2} a^{3} - \frac{5}{2} a - 1\) , \( -\frac{1}{2} a^{3} + a^{2} + \frac{3}{2} a - 3\) , \( a\) , \( a^{3} + \frac{3}{2} a^{2} - \frac{9}{2} a + 1\) , \( \frac{3}{2} a^{3} + \frac{5}{2} a^{2} - 5 a - 3\bigr] \)
|
| 8.1-a2
| \( \bigl[\frac{1}{2} a^{2} + \frac{1}{2} a - 1\) , \( -\frac{1}{2} a^{3} + a^{2} + \frac{3}{2} a - 4\) , \( \frac{1}{2} a^{3} - \frac{7}{2} a - 1\) , \( -2 a^{3} - 4 a^{2} + 5 a + 8\) , \( -\frac{17}{2} a^{3} - 12 a^{2} + \frac{47}{2} a + 8\bigr] \)
|
| 8.1-a3
| \( \bigl[\frac{1}{2} a^{2} + \frac{1}{2} a - 1\) , \( -\frac{1}{2} a^{3} + a^{2} + \frac{3}{2} a - 4\) , \( 0\) , \( \frac{3}{2} a^{3} - a^{2} - \frac{23}{2} a + 1\) , \( a^{3} - 8 a - 5\bigr] \)
|
| 8.1-a4
| \( \bigl[\frac{1}{2} a^{2} + \frac{1}{2} a - 1\) , \( -\frac{1}{2} a^{2} + \frac{1}{2} a + 3\) , \( 0\) , \( \frac{7}{2} a^{3} - 6 a^{2} - \frac{39}{2} a + 28\) , \( \frac{27}{2} a^{3} - \frac{59}{2} a^{2} - 81 a + 128\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrr}
1 & 2 & 3 & 6 \\
2 & 1 & 6 & 3 \\
3 & 6 & 1 & 2 \\
6 & 3 & 2 & 1
\end{array}\right)\)
