Elliptic curves in class 8.1-b over 4.4.13968.1
Isogeny class 8.1-b contains
4 curves linked by isogenies of
degrees dividing 6.
| Curve label |
Weierstrass Coefficients |
| 8.1-b1
| \( \bigl[\frac{1}{2} a^{3} - \frac{5}{2} a - 1\) , \( -\frac{1}{2} a^{3} + a^{2} + \frac{3}{2} a - 3\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - 1\) , \( 4 a^{3} - \frac{9}{2} a^{2} - \frac{47}{2} a + 27\) , \( -11 a^{3} + \frac{67}{2} a^{2} + \frac{145}{2} a - 136\bigr] \)
|
| 8.1-b2
| \( \bigl[\frac{1}{2} a^{3} - \frac{5}{2} a - 1\) , \( -\frac{1}{2} a^{2} + \frac{1}{2} a + 1\) , \( \frac{1}{2} a^{2} + \frac{1}{2} a - 1\) , \( -a^{3} - a^{2} + 5 a + 2\) , \( -\frac{1}{2} a^{3} + \frac{1}{2} a^{2} + a\bigr] \)
|
| 8.1-b3
| \( \bigl[\frac{1}{2} a^{3} - \frac{5}{2} a - 1\) , \( -\frac{1}{2} a^{2} + \frac{1}{2} a + 1\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 2 a + 2\) , \( 2 a^{3} + a^{2} - 10 a - 4\) , \( \frac{5}{2} a^{3} + \frac{9}{2} a^{2} - 4 a - 4\bigr] \)
|
| 8.1-b4
| \( \bigl[\frac{1}{2} a^{2} + \frac{1}{2} a - 1\) , \( -\frac{1}{2} a^{2} + \frac{1}{2} a + 3\) , \( \frac{1}{2} a^{3} - \frac{5}{2} a - 1\) , \( -\frac{1}{2} a^{2} - \frac{1}{2} a + 2\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 4 a - 1\bigr] \)
|
Rank: \( 1 \)
\(\left(\begin{array}{rrrr}
1 & 3 & 2 & 6 \\
3 & 1 & 6 & 2 \\
2 & 6 & 1 & 3 \\
6 & 2 & 3 & 1
\end{array}\right)\)
