Elliptic curves in class 8.2-b over 4.4.13968.1
Isogeny class 8.2-b contains
4 curves linked by isogenies of
degrees dividing 6.
| Curve label |
Weierstrass Coefficients |
| 8.2-b1
| \( \bigl[\frac{1}{2} a^{2} + \frac{1}{2} a - 2\) , \( -\frac{1}{2} a^{3} + a^{2} + \frac{7}{2} a - 3\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 2 a + 1\) , \( 2 a^{3} - 16 a - 14\) , \( -\frac{21}{2} a^{3} + \frac{15}{2} a^{2} + 83 a + 24\bigr] \)
|
| 8.2-b2
| \( \bigl[\frac{1}{2} a^{2} + \frac{1}{2} a - 2\) , \( -\frac{1}{2} a^{3} + \frac{1}{2} a^{2} + 4 a - 1\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - 1\) , \( -\frac{1}{2} a^{3} + a^{2} + \frac{9}{2} a - 2\) , \( \frac{1}{2} a^{2} + \frac{1}{2} a\bigr] \)
|
| 8.2-b3
| \( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 2 a + 1\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - 3\) , \( \frac{1}{2} a^{2} + \frac{1}{2} a - 2\) , \( -2 a^{3} + 3 a^{2} + 19 a + 6\) , \( \frac{27}{2} a^{3} - 6 a^{2} - \frac{197}{2} a - 33\bigr] \)
|
| 8.2-b4
| \( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 2 a + 1\) , \( -\frac{1}{2} a^{3} + \frac{1}{2} a^{2} + 2 a - 1\) , \( \frac{1}{2} a^{3} - \frac{7}{2} a - 1\) , \( -\frac{3}{2} a^{3} + \frac{7}{2} a^{2} + 5 a - 12\) , \( 2 a^{3} - 4 a^{2} - 15 a + 18\bigr] \)
|
Rank: \( 1 \)
\(\left(\begin{array}{rrrr}
1 & 2 & 3 & 6 \\
2 & 1 & 6 & 3 \\
3 & 6 & 1 & 2 \\
6 & 3 & 2 & 1
\end{array}\right)\)
