Elliptic curves in class 11.1-e over 6.6.1312625.1
Isogeny class 11.1-e contains
6 curves linked by isogenies of
degrees dividing 8.
| Curve label |
Weierstrass Coefficients |
| 11.1-e1
| \( \bigl[a^{3} - 3 a + 1\) , \( a^{4} - 6 a^{2} + a + 6\) , \( a^{3} - 3 a + 2\) , \( 110 a^{5} + 72 a^{4} - 708 a^{3} - 340 a^{2} + 1015 a + 93\) , \( 802 a^{5} + 296 a^{4} - 4904 a^{3} - 1455 a^{2} + 6306 a + 506\bigr] \)
|
| 11.1-e2
| \( \bigl[a^{3} - 3 a + 1\) , \( a^{4} - 6 a^{2} + a + 6\) , \( a^{3} - 3 a + 2\) , \( 10 a^{5} + 7 a^{4} - 63 a^{3} - 35 a^{2} + 85 a + 18\) , \( -9 a^{5} - 6 a^{4} + 59 a^{3} + 26 a^{2} - 88 a\bigr] \)
|
| 11.1-e3
| \( \bigl[a^{5} + a^{4} - 7 a^{3} - 5 a^{2} + 12 a + 3\) , \( -a^{4} + 4 a^{2} + a - 1\) , \( -a^{5} + 7 a^{3} - 11 a + 2\) , \( 2 a^{5} - 2 a^{4} - 15 a^{3} + 11 a^{2} + 26 a - 10\) , \( -3 a^{2} + 10\bigr] \)
|
| 11.1-e4
| \( \bigl[a^{4} - 4 a^{2} + 1\) , \( a^{3} - 2 a\) , \( a^{3} - 2 a + 1\) , \( -10 a^{5} - 13 a^{4} + 79 a^{3} + 43 a^{2} - 119 a - 10\) , \( -55 a^{5} + 127 a^{4} + 102 a^{3} - 339 a^{2} + 145 a + 13\bigr] \)
|
| 11.1-e5
| \( \bigl[a^{5} + a^{4} - 6 a^{3} - 5 a^{2} + 8 a + 4\) , \( a^{5} + a^{4} - 8 a^{3} - 5 a^{2} + 14 a + 3\) , \( a^{5} + a^{4} - 7 a^{3} - 5 a^{2} + 12 a + 4\) , \( -a^{5} - 2 a^{4} + 9 a^{3} + 7 a^{2} - 17 a - 3\) , \( -5 a^{5} - 2 a^{4} + 35 a^{3} + 9 a^{2} - 56 a - 6\bigr] \)
|
| 11.1-e6
| \( \bigl[a^{4} - 5 a^{2} + a + 5\) , \( a^{5} - 6 a^{3} + a^{2} + 7 a - 4\) , \( 1\) , \( 18 a^{5} - 59 a^{4} - 7 a^{3} + 168 a^{2} - 115 a - 17\) , \( 232 a^{5} - 698 a^{4} - 224 a^{3} + 2072 a^{2} - 1346 a - 115\bigr] \)
|
Rank: \( 1 \)
\(\left(\begin{array}{rrrrrr}
1 & 2 & 8 & 4 & 4 & 8 \\
2 & 1 & 4 & 2 & 2 & 4 \\
8 & 4 & 1 & 8 & 2 & 4 \\
4 & 2 & 8 & 1 & 4 & 8 \\
4 & 2 & 2 & 4 & 1 & 2 \\
8 & 4 & 4 & 8 & 2 & 1
\end{array}\right)\)
