Elliptic curves in class 16.1-a over 4.4.13888.1
Isogeny class 16.1-a contains
4 curves linked by isogenies of
degrees dividing 6.
| Curve label |
Weierstrass Coefficients |
| 16.1-a1
| \( \bigl[a^{2} - a - 3\) , \( a - 1\) , \( 0\) , \( \frac{2}{3} a^{3} + \frac{2}{3} a^{2} - \frac{5}{3} a - 1\) , \( 0\bigr] \)
|
| 16.1-a2
| \( \bigl[a^{2} - a - 3\) , \( a - 1\) , \( 0\) , \( -\frac{8}{3} a^{3} - \frac{8}{3} a^{2} + \frac{20}{3} a + 4\) , \( -\frac{58}{3} a^{3} - \frac{82}{3} a^{2} + \frac{148}{3} a + 56\bigr] \)
|
| 16.1-a3
| \( \bigl[\frac{1}{3} a^{3} - \frac{2}{3} a^{2} - \frac{4}{3} a + 1\) , \( -\frac{1}{3} a^{3} + \frac{5}{3} a^{2} + \frac{4}{3} a - 6\) , \( \frac{1}{3} a^{3} - \frac{2}{3} a^{2} - \frac{4}{3} a + 1\) , \( -\frac{79}{3} a^{3} + \frac{230}{3} a^{2} + \frac{346}{3} a - 264\) , \( 218 a^{3} - 633 a^{2} - 954 a + 2170\bigr] \)
|
| 16.1-a4
| \( \bigl[\frac{1}{3} a^{3} - \frac{2}{3} a^{2} - \frac{4}{3} a + 1\) , \( -\frac{1}{3} a^{3} + \frac{5}{3} a^{2} + \frac{4}{3} a - 6\) , \( \frac{1}{3} a^{3} - \frac{2}{3} a^{2} - \frac{4}{3} a + 1\) , \( 2 a^{3} - 5 a^{2} - 8 a + 16\) , \( \frac{25}{3} a^{3} - \frac{71}{3} a^{2} - \frac{109}{3} a + 81\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrr}
1 & 2 & 6 & 3 \\
2 & 1 & 3 & 6 \\
6 & 3 & 1 & 2 \\
3 & 6 & 2 & 1
\end{array}\right)\)
