Elliptic curves in class 27225.5-b over \(\Q(\sqrt{-11}) \)
Isogeny class 27225.5-b contains
8 curves linked by isogenies of
degrees dividing 12.
| Curve label |
Weierstrass Coefficients |
| 27225.5-b1
| \( \bigl[a\) , \( -a - 1\) , \( a + 1\) , \( -24 a - 15\) , \( -57 a + 14\bigr] \)
|
| 27225.5-b2
| \( \bigl[a + 1\) , \( 1\) , \( 1\) , \( 24 a - 42\) , \( 80 a - 84\bigr] \)
|
| 27225.5-b3
| \( \bigl[a\) , \( -a - 1\) , \( a + 1\) , \( -24 a + 40\) , \( -167 a - 217\bigr] \)
|
| 27225.5-b4
| \( \bigl[a + 1\) , \( 1\) , \( 1\) , \( 24 a + 13\) , \( 190 a - 370\bigr] \)
|
| 27225.5-b5
| \( \bigl[a + 1\) , \( 1\) , \( 1\) , \( -361 a + 233\) , \( 1708 a - 5056\bigr] \)
|
| 27225.5-b6
| \( \bigl[a\) , \( -a - 1\) , \( a + 1\) , \( 361 a - 125\) , \( -2070 a - 3220\bigr] \)
|
| 27225.5-b7
| \( \bigl[a + 1\) , \( 1\) , \( 1\) , \( 409 a + 673\) , \( 5052 a - 14428\bigr] \)
|
| 27225.5-b8
| \( \bigl[a\) , \( -a - 1\) , \( a + 1\) , \( -409 a + 1085\) , \( -4644 a - 10458\bigr] \)
|
Rank: \( 2 \)
\(\left(\begin{array}{rrrrrrrr}
1 & 3 & 2 & 6 & 12 & 4 & 12 & 4 \\
3 & 1 & 6 & 2 & 4 & 12 & 4 & 12 \\
2 & 6 & 1 & 3 & 6 & 2 & 6 & 2 \\
6 & 2 & 3 & 1 & 2 & 6 & 2 & 6 \\
12 & 4 & 6 & 2 & 1 & 12 & 4 & 3 \\
4 & 12 & 2 & 6 & 12 & 1 & 3 & 4 \\
12 & 4 & 6 & 2 & 4 & 3 & 1 & 12 \\
4 & 12 & 2 & 6 & 3 & 4 & 12 & 1
\end{array}\right)\)
