Elliptic curves in class 8.4-b over 4.4.13968.1
Isogeny class 8.4-b contains
4 curves linked by isogenies of
degrees dividing 4.
| Curve label |
Weierstrass Coefficients |
| 8.4-b1
| \( \bigl[\frac{1}{2} a^{3} - \frac{5}{2} a - 1\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 2 a + 1\) , \( a\) , \( 3 a^{3} + 10 a^{2} - 2 a - 22\) , \( 16 a^{3} + 13 a^{2} - 52 a + 4\bigr] \)
|
| 8.4-b2
| \( \bigl[\frac{1}{2} a^{2} + \frac{1}{2} a - 1\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 3 a\) , \( \frac{1}{2} a^{2} + \frac{1}{2} a - 1\) , \( \frac{37}{2} a^{3} - 11 a^{2} - \frac{281}{2} a - 48\) , \( \frac{165}{2} a^{3} - 51 a^{2} - \frac{1281}{2} a - 214\bigr] \)
|
| 8.4-b3
| \( \bigl[\frac{1}{2} a^{2} + \frac{1}{2} a - 1\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 3 a\) , \( \frac{1}{2} a^{2} + \frac{1}{2} a - 1\) , \( a^{3} + \frac{3}{2} a^{2} - \frac{11}{2} a - 8\) , \( \frac{3}{2} a^{3} + a^{2} - \frac{11}{2} a\bigr] \)
|
| 8.4-b4
| \( \bigl[\frac{1}{2} a^{2} + \frac{1}{2} a - 1\) , \( -\frac{1}{2} a^{2} + \frac{1}{2} a + 1\) , \( a\) , \( -a^{3} + 5 a + 2\) , \( -a^{3} - 3 a^{2} - a\bigr] \)
|
Rank: \( 1 \)
\(\left(\begin{array}{rrrr}
1 & 4 & 2 & 4 \\
4 & 1 & 2 & 4 \\
2 & 2 & 1 & 2 \\
4 & 4 & 2 & 1
\end{array}\right)\)
