Elliptic curves in class 11.1-d over 6.6.1312625.1
Isogeny class 11.1-d contains
6 curves linked by isogenies of
degrees dividing 8.
| Curve label |
Weierstrass Coefficients |
| 11.1-d1
| \( \bigl[a^{3} + a^{2} - 2 a - 1\) , \( -2 a^{5} - a^{4} + 13 a^{3} + 5 a^{2} - 18 a - 2\) , \( a^{5} - 6 a^{3} + 9 a\) , \( 225 a^{5} + 111 a^{4} - 1404 a^{3} - 518 a^{2} + 1905 a + 137\) , \( 2618 a^{5} + 1291 a^{4} - 16396 a^{3} - 6158 a^{2} + 22202 a + 1736\bigr] \)
|
| 11.1-d2
| \( \bigl[a^{3} + a^{2} - 2 a - 1\) , \( -2 a^{5} - a^{4} + 13 a^{3} + 5 a^{2} - 18 a - 2\) , \( a^{5} - 6 a^{3} + 9 a\) , \( 15 a^{5} + 11 a^{4} - 84 a^{3} - 38 a^{2} + 110 a + 7\) , \( 74 a^{5} + 45 a^{4} - 441 a^{3} - 182 a^{2} + 590 a + 47\bigr] \)
|
| 11.1-d3
| \( \bigl[a^{3} - 2 a + 2\) , \( -2 a^{5} - a^{4} + 13 a^{3} + 6 a^{2} - 19 a - 7\) , \( a^{3} - 2 a + 2\) , \( 3 a^{5} + 3 a^{4} - 19 a^{3} - 12 a^{2} + 30 a + 8\) , \( 4 a^{5} - 5 a^{4} - 8 a^{3} + 18 a^{2} - 8 a - 7\bigr] \)
|
| 11.1-d4
| \( \bigl[a^{5} + a^{4} - 7 a^{3} - 5 a^{2} + 11 a + 4\) , \( 2 a^{5} + a^{4} - 13 a^{3} - 4 a^{2} + 18 a - 1\) , \( 2 a^{5} + a^{4} - 13 a^{3} - 4 a^{2} + 20 a\) , \( -3 a^{5} + 20 a^{3} - a^{2} - 28 a\) , \( -3 a^{5} + a^{4} + 17 a^{3} - 4 a^{2} - 19 a - 2\bigr] \)
|
| 11.1-d5
| \( \bigl[a^{5} + a^{4} - 7 a^{3} - 5 a^{2} + 12 a + 4\) , \( a^{5} + a^{4} - 6 a^{3} - 5 a^{2} + 7 a + 3\) , \( -a^{5} + 7 a^{3} + a^{2} - 11 a - 2\) , \( 71 a^{5} + 68 a^{4} - 346 a^{3} - 161 a^{2} + 451 a - 20\) , \( -390 a^{5} - 366 a^{4} + 1908 a^{3} + 858 a^{2} - 2478 a + 149\bigr] \)
|
| 11.1-d6
| \( \bigl[a^{4} - 4 a^{2} + 2\) , \( a^{2} - 2\) , \( -a^{5} + 7 a^{3} + a^{2} - 10 a - 2\) , \( -3 a^{5} - 2 a^{4} + 15 a^{3} + 11 a^{2} - 16 a - 15\) , \( -11 a^{5} + a^{4} + 73 a^{3} - 8 a^{2} - 113 a + 19\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrrrr}
1 & 2 & 4 & 4 & 8 & 8 \\
2 & 1 & 2 & 2 & 4 & 4 \\
4 & 2 & 1 & 4 & 8 & 8 \\
4 & 2 & 4 & 1 & 2 & 2 \\
8 & 4 & 8 & 2 & 1 & 4 \\
8 & 4 & 8 & 2 & 4 & 1
\end{array}\right)\)
