Elliptic curves in class 4.2-a over 4.4.13968.1
Isogeny class 4.2-a contains
6 curves linked by isogenies of
degrees dividing 18.
| Curve label |
Weierstrass Coefficients |
| 4.2-a1
| \( \bigl[\frac{1}{2} a^{2} - \frac{1}{2} a - 2\) , \( \frac{1}{2} a^{3} - \frac{7}{2} a\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - 1\) , \( -\frac{5}{2} a^{3} - 2 a^{2} + \frac{21}{2} a + 5\) , \( -\frac{3}{2} a^{3} - \frac{9}{2} a^{2} - 2 a\bigr] \)
|
| 4.2-a2
| \( \bigl[\frac{1}{2} a^{2} - \frac{1}{2} a - 2\) , \( \frac{1}{2} a^{3} - \frac{7}{2} a\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - 1\) , \( -130 a^{3} - 177 a^{2} + 338 a + 150\) , \( 3441 a^{3} + \frac{8919}{2} a^{2} - \frac{19019}{2} a - 4143\bigr] \)
|
| 4.2-a3
| \( \bigl[\frac{1}{2} a^{2} - \frac{1}{2} a - 2\) , \( -\frac{1}{2} a^{3} + \frac{7}{2} a\) , \( 0\) , \( \frac{5}{2} a^{3} - 10 a^{2} + \frac{11}{2} a + 11\) , \( -4 a^{3} + 14 a^{2} - a - 12\bigr] \)
|
| 4.2-a4
| \( \bigl[\frac{1}{2} a^{2} - \frac{1}{2} a - 2\) , \( -\frac{1}{2} a^{3} + \frac{7}{2} a\) , \( 0\) , \( 130 a^{3} - \frac{1135}{2} a^{2} + \frac{821}{2} a + 181\) , \( -\frac{7633}{2} a^{3} + \frac{32761}{2} a^{2} - 10724 a - 6446\bigr] \)
|
| 4.2-a5
| \( \bigl[\frac{1}{2} a^{3} - \frac{7}{2} a\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 2 a\) , \( a + 1\) , \( -179 a^{3} - 230 a^{2} + 505 a + 219\) , \( -5998 a^{3} - 7664 a^{2} + 16873 a + 7320\bigr] \)
|
| 4.2-a6
| \( \bigl[\frac{1}{2} a^{3} - \frac{7}{2} a\) , \( -\frac{1}{2} a^{3} + \frac{5}{2} a + 2\) , \( \frac{1}{2} a^{3} - \frac{5}{2} a - 1\) , \( -\frac{135}{2} a^{3} + \frac{323}{2} a^{2} + 411 a - 730\) , \( -\frac{1619}{2} a^{3} + \frac{3905}{2} a^{2} + 4916 a - 8604\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrrrr}
1 & 3 & 2 & 6 & 6 & 3 \\
3 & 1 & 6 & 2 & 18 & 9 \\
2 & 6 & 1 & 3 & 3 & 6 \\
6 & 2 & 3 & 1 & 9 & 18 \\
6 & 18 & 3 & 9 & 1 & 2 \\
3 & 9 & 6 & 18 & 2 & 1
\end{array}\right)\)
