Elliptic curves in class 16.1-b over 4.4.2225.1
Isogeny class 16.1-b contains
8 curves linked by isogenies of
degrees dividing 20.
| Curve label |
Weierstrass Coefficients |
| 16.1-b1
| \( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - 3\) , \( 1\) , \( 0\) , \( -\frac{91}{2} a^{3} - \frac{131}{2} a^{2} + \frac{145}{2} a + 64\) , \( -\frac{1923}{2} a^{3} - \frac{2783}{2} a^{2} + \frac{2849}{2} a + 1546\bigr] \)
|
| 16.1-b2
| \( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{3}{2} a - 3\) , \( -a^{2} + 2 a + 3\) , \( a^{2} - a - 3\) , \( 7 a^{3} + 11 a^{2} - 12 a - 132\) , \( -\frac{31}{2} a^{3} + \frac{449}{2} a^{2} + \frac{27}{2} a - 1143\bigr] \)
|
| 16.1-b3
| \( \bigl[a^{2} - 3\) , \( -\frac{1}{2} a^{3} + \frac{3}{2} a^{2} + \frac{1}{2} a - 3\) , \( a^{2} - 3\) , \( \frac{1373}{2} a^{3} - \frac{4061}{2} a^{2} + \frac{341}{2} a + 1401\) , \( \frac{57843}{2} a^{3} - \frac{160487}{2} a^{2} - \frac{7077}{2} a + 65326\bigr] \)
|
| 16.1-b4
| \( \bigl[a^{2} - 3\) , \( -a^{2} + 2\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - 2\) , \( -a^{3} - 4 a^{2} - 3 a + 2\) , \( \frac{7}{2} a^{3} + \frac{9}{2} a^{2} - \frac{11}{2} a - 5\bigr] \)
|
| 16.1-b5
| \( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{1}{2} a\) , \( -\frac{1}{2} a^{3} + \frac{3}{2} a^{2} - \frac{1}{2} a - 2\) , \( a^{2} - 3\) , \( -a^{3} - 9 a^{2} + 22 a - 12\) , \( \frac{141}{2} a^{3} - \frac{347}{2} a^{2} - \frac{121}{2} a + 189\bigr] \)
|
| 16.1-b6
| \( \bigl[a + 1\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - 4\) , \( a^{2} - 2\) , \( 507 a^{3} + 75 a^{2} - 2471 a - 1833\) , \( 11504 a^{3} + 1595 a^{2} - 55760 a - 40525\bigr] \)
|
| 16.1-b7
| \( \bigl[a + 1\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - 4\) , \( a^{2} - 2\) , \( 2 a^{3} - 11 a - 8\) , \( -10 a^{3} - 2 a^{2} + 48 a + 36\bigr] \)
|
| 16.1-b8
| \( \bigl[a + 1\) , \( a^{2} - 2 a - 3\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - 3\) , \( a^{3} - 7 a^{2} + 8 a + 6\) , \( -3 a^{3} + 11 a^{2} - 5 a - 10\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrrrrrr}
1 & 4 & 4 & 20 & 20 & 2 & 10 & 5 \\
4 & 1 & 4 & 5 & 20 & 2 & 10 & 20 \\
4 & 4 & 1 & 20 & 5 & 2 & 10 & 20 \\
20 & 5 & 20 & 1 & 4 & 10 & 2 & 4 \\
20 & 20 & 5 & 4 & 1 & 10 & 2 & 4 \\
2 & 2 & 2 & 10 & 10 & 1 & 5 & 10 \\
10 & 10 & 10 & 2 & 2 & 5 & 1 & 2 \\
5 & 20 & 20 & 4 & 4 & 10 & 2 & 1
\end{array}\right)\)
