Elliptic curves in class 20.1-c over 4.4.10025.1
Isogeny class 20.1-c contains
6 curves linked by isogenies of
degrees dividing 8.
| Curve label |
Weierstrass Coefficients |
| 20.1-c1
| \( \bigl[\frac{1}{2} a^{3} + \frac{3}{2} a^{2} - \frac{7}{2} a - 8\) , \( a + 1\) , \( a^{3} + 2 a^{2} - 6 a - 11\) , \( \frac{11}{2} a^{3} - \frac{25}{2} a^{2} - \frac{9}{2} a + 11\) , \( \frac{55}{2} a^{3} - \frac{173}{2} a^{2} - \frac{1}{2} a + 121\bigr] \)
|
| 20.1-c2
| \( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{7}{2} a - 3\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{7}{2} a - 4\) , \( \frac{1}{2} a^{3} + \frac{3}{2} a^{2} - \frac{5}{2} a - 7\) , \( -\frac{99}{2} a^{3} - \frac{165}{2} a^{2} + \frac{649}{2} a + 372\) , \( 114 a^{3} + 189 a^{2} - 753 a - 862\bigr] \)
|
| 20.1-c3
| \( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - 3\) , \( -a + 1\) , \( 1\) , \( -a^{3} + 4 a + 4\) , \( \frac{1}{2} a^{3} + \frac{3}{2} a^{2} - \frac{9}{2} a - 5\bigr] \)
|
| 20.1-c4
| \( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{7}{2} a - 2\) , \( -\frac{1}{2} a^{3} - \frac{1}{2} a^{2} + \frac{7}{2} a + 4\) , \( a^{3} + 2 a^{2} - 6 a - 10\) , \( -\frac{167}{2} a^{3} - \frac{267}{2} a^{2} + \frac{1133}{2} a + 642\) , \( -300 a^{3} - 549 a^{2} + 1768 a + 2093\bigr] \)
|
| 20.1-c5
| \( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{7}{2} a - 2\) , \( -\frac{1}{2} a^{3} - \frac{1}{2} a^{2} + \frac{7}{2} a + 4\) , \( 0\) , \( -12 a^{3} + 21 a^{2} + 73 a - 128\) , \( -238 a^{3} + 959 a^{2} - 242 a - 1652\bigr] \)
|
| 20.1-c6
| \( \bigl[1\) , \( -1\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{7}{2} a - 2\) , \( \frac{109}{2} a^{3} - \frac{443}{2} a^{2} + \frac{139}{2} a + 356\) , \( -1213 a^{3} + 4874 a^{2} - 1366 a - 8026\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrrrr}
1 & 2 & 8 & 4 & 8 & 4 \\
2 & 1 & 4 & 2 & 4 & 2 \\
8 & 4 & 1 & 8 & 4 & 2 \\
4 & 2 & 8 & 1 & 8 & 4 \\
8 & 4 & 4 & 8 & 1 & 2 \\
4 & 2 & 2 & 4 & 2 & 1
\end{array}\right)\)
