Elliptic curves in class 12.1-b over \(\Q(\sqrt{33}) \)
Isogeny class 12.1-b contains
12 curves linked by isogenies of
degrees dividing 36.
| Curve label |
Weierstrass Coefficients |
| 12.1-b1
| \( \bigl[1\) , \( 0\) , \( a + 1\) , \( -23 a - 171\) , \( -182 a - 930\bigr] \)
|
| 12.1-b2
| \( \bigl[1\) , \( 0\) , \( a + 1\) , \( -23 a - 66\) , \( 133 a + 330\bigr] \)
|
| 12.1-b3
| \( \bigl[1\) , \( 0\) , \( a + 1\) , \( 2 a + 4\) , \( -2 a - 6\bigr] \)
|
| 12.1-b4
| \( \bigl[1\) , \( a + 1\) , \( 0\) , \( 27 a - 84\) , \( -63 a + 216\bigr] \)
|
| 12.1-b5
| \( \bigl[1\) , \( a + 1\) , \( 0\) , \( 28022 a - 94494\) , \( -4337718 a + 14628006\bigr] \)
|
| 12.1-b6
| \( \bigl[1\) , \( a + 1\) , \( 0\) , \( -4468 a - 10599\) , \( -277078 a - 657307\bigr] \)
|
| 12.1-b7
| \( \bigl[1\) , \( a + 1\) , \( 0\) , \( -533 a - 1264\) , \( 10417 a + 24712\bigr] \)
|
| 12.1-b8
| \( \bigl[1\) , \( a + 1\) , \( 0\) , \( 347 a - 1164\) , \( -6063 a + 20448\bigr] \)
|
| 12.1-b9
| \( \bigl[1\) , \( a + 1\) , \( 0\) , \( 1752 a - 5904\) , \( -68268 a + 230220\bigr] \)
|
| 12.1-b10
| \( \bigl[1\) , \( a + 1\) , \( 0\) , \( 1062 a - 3579\) , \( 31512 a - 106275\bigr] \)
|
| 12.1-b11
| \( \bigl[1\) , \( a + 1\) , \( 0\) , \( -43108 a - 102264\) , \( 8190752 a + 19430768\bigr] \)
|
| 12.1-b12
| \( \bigl[1\) , \( a + 1\) , \( 0\) , \( 1112 a - 3819\) , \( 27462 a - 92979\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrrrrrrrrrr}
1 & 9 & 3 & 6 & 36 & 4 & 12 & 12 & 18 & 2 & 36 & 4 \\
9 & 1 & 3 & 6 & 4 & 36 & 12 & 12 & 2 & 18 & 4 & 36 \\
3 & 3 & 1 & 2 & 12 & 12 & 4 & 4 & 6 & 6 & 12 & 12 \\
6 & 6 & 2 & 1 & 6 & 6 & 2 & 2 & 3 & 3 & 6 & 6 \\
36 & 4 & 12 & 6 & 1 & 36 & 12 & 3 & 2 & 18 & 4 & 9 \\
4 & 36 & 12 & 6 & 36 & 1 & 3 & 12 & 18 & 2 & 9 & 4 \\
12 & 12 & 4 & 2 & 12 & 3 & 1 & 4 & 6 & 6 & 3 & 12 \\
12 & 12 & 4 & 2 & 3 & 12 & 4 & 1 & 6 & 6 & 12 & 3 \\
18 & 2 & 6 & 3 & 2 & 18 & 6 & 6 & 1 & 9 & 2 & 18 \\
2 & 18 & 6 & 3 & 18 & 2 & 6 & 6 & 9 & 1 & 18 & 2 \\
36 & 4 & 12 & 6 & 4 & 9 & 3 & 12 & 2 & 18 & 1 & 36 \\
4 & 36 & 12 & 6 & 9 & 4 & 12 & 3 & 18 & 2 & 36 & 1
\end{array}\right)\)
