Elliptic curves in class 4.2-f over 4.4.13968.1
Isogeny class 4.2-f contains
6 curves linked by isogenies of
degrees dividing 18.
| Curve label |
Weierstrass Coefficients |
| 4.2-f1
| \( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 3 a + 1\) , \( -\frac{1}{2} a^{3} + \frac{7}{2} a + 1\) , \( \frac{1}{2} a^{3} - \frac{7}{2} a - 1\) , \( -181 a^{3} - \frac{465}{2} a^{2} + \frac{1025}{2} a + 222\) , \( \frac{10455}{2} a^{3} + 6681 a^{2} - \frac{29421}{2} a - 6382\bigr] \)
|
| 4.2-f2
| \( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 3 a + 1\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 4 a + 2\) , \( \frac{1}{2} a^{2} + \frac{1}{2} a - 1\) , \( -\frac{131}{2} a^{3} + 160 a^{2} + \frac{799}{2} a - 727\) , \( \frac{1353}{2} a^{3} - \frac{3261}{2} a^{2} - 4104 a + 7142\bigr] \)
|
| 4.2-f3
| \( \bigl[1\) , \( \frac{1}{2} a^{3} - \frac{7}{2} a - 1\) , \( 0\) , \( \frac{5}{2} a^{3} - 10 a^{2} + \frac{11}{2} a + 11\) , \( 4 a^{3} - 14 a^{2} + a + 12\bigr] \)
|
| 4.2-f4
| \( \bigl[1\) , \( \frac{1}{2} a^{3} - \frac{7}{2} a - 1\) , \( 0\) , \( 130 a^{3} - \frac{1135}{2} a^{2} + \frac{821}{2} a + 181\) , \( \frac{7633}{2} a^{3} - \frac{32761}{2} a^{2} + 10724 a + 6446\bigr] \)
|
| 4.2-f5
| \( \bigl[1\) , \( -\frac{1}{2} a^{3} + \frac{7}{2} a + 2\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - 2\) , \( -\frac{7}{2} a^{3} - 2 a^{2} + \frac{35}{2} a + 8\) , \( -\frac{3}{2} a^{3} + \frac{5}{2} a^{2} + 16 a + 5\bigr] \)
|
| 4.2-f6
| \( \bigl[1\) , \( -\frac{1}{2} a^{3} + \frac{7}{2} a + 2\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - 2\) , \( -131 a^{3} - 177 a^{2} + 345 a + 153\) , \( -\frac{7143}{2} a^{3} - \frac{9273}{2} a^{2} + 9851 a + 4293\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrrrr}
1 & 2 & 3 & 9 & 6 & 18 \\
2 & 1 & 6 & 18 & 3 & 9 \\
3 & 6 & 1 & 3 & 2 & 6 \\
9 & 18 & 3 & 1 & 6 & 2 \\
6 & 3 & 2 & 6 & 1 & 3 \\
18 & 9 & 6 & 2 & 3 & 1
\end{array}\right)\)
