Elliptic curves in class 16.1-a over 4.4.2624.1
Isogeny class 16.1-a contains
6 curves linked by isogenies of
degrees dividing 8.
| Curve label |
Weierstrass Coefficients |
| 16.1-a1
| \( \bigl[a^{2} - a - 1\) , \( -a^{3} + 2 a^{2} + 2 a - 1\) , \( a^{3} - a^{2} - 3 a\) , \( -4 a^{3} + 9 a^{2} + 7 a - 12\) , \( 7 a^{3} - 17 a^{2} - 16 a + 19\bigr] \)
|
| 16.1-a2
| \( \bigl[a^{2} - a - 1\) , \( -a^{3} + 2 a^{2} + 2 a - 1\) , \( a^{3} - a^{2} - 3 a\) , \( 16 a^{3} - 31 a^{2} - 48 a + 18\) , \( 15 a^{3} - 49 a^{2} - 13 a + 86\bigr] \)
|
| 16.1-a3
| \( \bigl[a^{2} - a - 1\) , \( -a^{2} + 3 a + 1\) , \( a^{2} - a - 1\) , \( -a^{3} + 3 a^{2} + 2 a - 1\) , \( -a^{2} + a\bigr] \)
|
| 16.1-a4
| \( \bigl[a^{3} - a^{2} - 3 a\) , \( -a^{3} + 2 a^{2} + a\) , \( a^{2} - a - 1\) , \( -a^{2} - a + 4\) , \( -5 a^{3} + 11 a^{2} + 11 a - 12\bigr] \)
|
| 16.1-a5
| \( \bigl[a^{3} - a^{2} - 3 a\) , \( -a^{2} + 2 a + 2\) , \( a^{3} - a^{2} - 3 a\) , \( 4 a^{3} - 10 a^{2} + 8 a + 1\) , \( -6 a^{3} + 47 a^{2} - 18 a - 12\bigr] \)
|
| 16.1-a6
| \( \bigl[0\) , \( a^{3} - a^{2} - 5 a + 1\) , \( 0\) , \( -6 a^{3} + 14 a^{2} + 12 a - 13\) , \( -13 a^{3} + 31 a^{2} + 27 a - 36\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrrrr}
1 & 2 & 4 & 4 & 2 & 2 \\
2 & 1 & 8 & 8 & 4 & 4 \\
4 & 8 & 1 & 4 & 8 & 2 \\
4 & 8 & 4 & 1 & 8 & 2 \\
2 & 4 & 8 & 8 & 1 & 4 \\
2 & 4 & 2 & 2 & 4 & 1
\end{array}\right)\)
