Elliptic curves in class 27.1-f over 4.4.11661.1
Isogeny class 27.1-f contains
4 curves linked by isogenies of
degrees dividing 6.
| Curve label |
Weierstrass Coefficients |
| 27.1-f1
| \( \bigl[a^{2} - a - 2\) , \( a^{3} - a^{2} - 4 a + 1\) , \( a^{3} - 5 a - 1\) , \( -8 a^{3} + 29 a^{2} - 17 a - 12\) , \( -59 a^{3} + 217 a^{2} - 121 a - 112\bigr] \)
|
| 27.1-f2
| \( \bigl[a^{2} - a - 2\) , \( a^{3} - a^{2} - 4 a + 1\) , \( a^{3} - 5 a - 1\) , \( 62 a^{3} - 226 a^{2} + 118 a + 118\) , \( -538 a^{3} + 1957 a^{2} - 1048 a - 990\bigr] \)
|
| 27.1-f3
| \( \bigl[a^{3} - 5 a - 1\) , \( a^{3} - a^{2} - 4 a + 1\) , \( a^{2} - 2\) , \( -687 a^{3} + 1699 a^{2} + 1945 a - 4356\) , \( 26168 a^{3} - 64720 a^{2} - 74043 a + 165881\bigr] \)
|
| 27.1-f4
| \( \bigl[1\) , \( a^{3} - 5 a - 2\) , \( a^{3} - 4 a - 1\) , \( 8 a^{3} - 35 a^{2} + 30 a + 18\) , \( -43 a^{3} + 157 a^{2} - 89 a - 79\bigr] \)
|
Rank: \( 1 \)
\(\left(\begin{array}{rrrr}
1 & 2 & 6 & 3 \\
2 & 1 & 3 & 6 \\
6 & 3 & 1 & 2 \\
3 & 6 & 2 & 1
\end{array}\right)\)
