Elliptic curves in class 16.2-a over 4.4.4913.1
Isogeny class 16.2-a contains
4 curves linked by isogenies of
degrees dividing 4.
| Curve label |
Weierstrass Coefficients |
| 16.2-a1
| \( \bigl[a^{2} - a - 3\) , \( -a^{3} + a^{2} + 4 a + 1\) , \( \frac{1}{2} a^{3} - 3 a - \frac{1}{2}\) , \( -\frac{15}{2} a^{3} - 8 a^{2} + 8 a + \frac{7}{2}\) , \( -\frac{61}{2} a^{3} - 53 a^{2} + 16 a + \frac{21}{2}\bigr] \)
|
| 16.2-a2
| \( \bigl[a^{2} - a - 3\) , \( -a^{3} + a^{2} + 4 a + 1\) , \( \frac{1}{2} a^{3} - 3 a - \frac{1}{2}\) , \( -\frac{5}{2} a^{3} + 2 a^{2} + 8 a + \frac{7}{2}\) , \( -2 a^{3} + 2 a^{2} + 7 a + 2\bigr] \)
|
| 16.2-a3
| \( \bigl[a^{2} - a - 3\) , \( -a^{3} + a^{2} + 4 a + 1\) , \( \frac{1}{2} a^{3} - 3 a - \frac{1}{2}\) , \( -\frac{5}{2} a^{3} - 8 a^{2} + 13 a + \frac{7}{2}\) , \( \frac{11}{2} a^{3} + 22 a^{2} + 7 a - \frac{7}{2}\bigr] \)
|
| 16.2-a4
| \( \bigl[-\frac{1}{2} a^{3} + a^{2} + 2 a - \frac{1}{2}\) , \( -\frac{1}{2} a^{3} + a^{2} + 3 a - \frac{1}{2}\) , \( \frac{1}{2} a^{3} - 3 a - \frac{1}{2}\) , \( \frac{1}{2} a^{3} - 3 a + \frac{5}{2}\) , \( -\frac{1}{2} a^{3} + a^{2} + 3 a - \frac{5}{2}\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrr}
1 & 2 & 4 & 4 \\
2 & 1 & 2 & 2 \\
4 & 2 & 1 & 4 \\
4 & 2 & 4 & 1
\end{array}\right)\)
