Elliptic curves in class 8.2-a over 4.4.13968.1
Isogeny class 8.2-a contains
4 curves linked by isogenies of
degrees dividing 6.
| Curve label |
Weierstrass Coefficients |
| 8.2-a1
| \( \bigl[\frac{1}{2} a^{2} + \frac{1}{2} a - 2\) , \( \frac{1}{2} a^{2} - \frac{3}{2} a - 3\) , \( 0\) , \( -\frac{3}{2} a^{3} + \frac{7}{2} a^{2} + 9 a - 10\) , \( -a^{3} + 3 a^{2} + 5 a - 12\bigr] \)
|
| 8.2-a2
| \( \bigl[\frac{1}{2} a^{2} + \frac{1}{2} a - 2\) , \( -\frac{1}{2} a^{3} + \frac{1}{2} a^{2} + 4 a - 1\) , \( \frac{1}{2} a^{3} - \frac{5}{2} a\) , \( -\frac{7}{2} a^{3} + 2 a^{2} + \frac{51}{2} a + 7\) , \( -14 a^{3} + 8 a^{2} + 108 a + 39\bigr] \)
|
| 8.2-a3
| \( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 2 a + 1\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - 3\) , \( 0\) , \( a^{3} + 2 a^{2} - 2 a - 3\) , \( 2 a^{3} + a^{2} - 6 a + 1\bigr] \)
|
| 8.2-a4
| \( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 2 a + 1\) , \( -1\) , \( a + 1\) , \( 2 a^{3} + \frac{3}{2} a^{2} - \frac{29}{2} a - 19\) , \( \frac{29}{2} a^{3} - 10 a^{2} - \frac{213}{2} a - 20\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrr}
1 & 2 & 3 & 6 \\
2 & 1 & 6 & 3 \\
3 & 6 & 1 & 2 \\
6 & 3 & 2 & 1
\end{array}\right)\)
