Elliptic curves in class 9.1-b over 4.4.12400.1
Isogeny class 9.1-b contains
4 curves linked by isogenies of
degrees dividing 6.
| Curve label |
Weierstrass Coefficients |
| 9.1-b1
| \( \bigl[a\) , \( -\frac{1}{2} a^{3} - \frac{1}{2} a^{2} + \frac{9}{2} a + \frac{5}{2}\) , \( 0\) , \( -8 a^{3} + 7 a^{2} + 64 a - 78\) , \( \frac{79}{2} a^{3} - 72 a^{2} - \frac{631}{2} a + 604\bigr] \)
|
| 9.1-b2
| \( \bigl[\frac{1}{2} a^{3} - \frac{7}{2} a\) , \( -\frac{1}{2} a^{2} - a + \frac{7}{2}\) , \( 1\) , \( -\frac{5}{2} a^{3} + \frac{9}{2} a^{2} + \frac{41}{2} a - \frac{71}{2}\) , \( \frac{7}{2} a^{3} - 7 a^{2} - \frac{57}{2} a + 56\bigr] \)
|
| 9.1-b3
| \( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - \frac{7}{2}\) , \( \frac{1}{2} a^{3} - \frac{7}{2} a + 1\) , \( \frac{1}{2} a^{3} - \frac{7}{2} a + 1\) , \( \frac{13}{2} a^{3} - a^{2} - \frac{75}{2} a - 15\) , \( -\frac{21}{2} a^{3} + 10 a^{2} + \frac{129}{2} a + 9\bigr] \)
|
| 9.1-b4
| \( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - \frac{7}{2}\) , \( \frac{1}{2} a^{3} - \frac{7}{2} a + 1\) , \( \frac{1}{2} a^{3} - \frac{7}{2} a + 1\) , \( \frac{3}{2} a^{3} + \frac{3}{2} a^{2} - \frac{15}{2} a - \frac{5}{2}\) , \( a^{3} + \frac{5}{2} a^{2} - 2 a - \frac{15}{2}\bigr] \)
|
Rank: \( 1 \)
\(\left(\begin{array}{rrrr}
1 & 2 & 3 & 6 \\
2 & 1 & 6 & 3 \\
3 & 6 & 1 & 2 \\
6 & 3 & 2 & 1
\end{array}\right)\)
