Elliptic curves in class 12.1-a over \(\Q(\sqrt{33}) \)
Isogeny class 12.1-a contains
12 curves linked by isogenies of
degrees dividing 36.
Curve label |
Weierstrass Coefficients |
12.1-a1
| \( \bigl[1\) , \( -a - 1\) , \( 1\) , \( 43110 a - 145374\) , \( -8233861 a + 27766893\bigr] \)
|
12.1-a2
| \( \bigl[1\) , \( -a - 1\) , \( 1\) , \( 4470 a - 15069\) , \( 272609 a - 919317\bigr] \)
|
12.1-a3
| \( \bigl[1\) , \( -a - 1\) , \( 1\) , \( 535 a - 1799\) , \( -10951 a + 36927\bigr] \)
|
12.1-a4
| \( \bigl[1\) , \( -a - 1\) , \( 1\) , \( -25 a - 59\) , \( 89 a + 211\bigr] \)
|
12.1-a5
| \( \bigl[1\) , \( -a - 1\) , \( 1\) , \( -1110 a - 2709\) , \( -26351 a - 62809\bigr] \)
|
12.1-a6
| \( \bigl[1\) , \( 0\) , \( a\) , \( 22 a - 88\) , \( -134 a + 464\bigr] \)
|
12.1-a7
| \( \bigl[1\) , \( 0\) , \( a\) , \( -3 a + 7\) , \( a - 7\bigr] \)
|
12.1-a8
| \( \bigl[1\) , \( -a - 1\) , \( 1\) , \( -345 a - 819\) , \( 6409 a + 15203\bigr] \)
|
12.1-a9
| \( \bigl[1\) , \( -a - 1\) , \( 1\) , \( -1060 a - 2519\) , \( -30451 a - 72245\bigr] \)
|
12.1-a10
| \( \bigl[1\) , \( -a - 1\) , \( 1\) , \( -1750 a - 4154\) , \( 70019 a + 166105\bigr] \)
|
12.1-a11
| \( \bigl[1\) , \( 0\) , \( a\) , \( 22 a - 193\) , \( 181 a - 1111\bigr] \)
|
12.1-a12
| \( \bigl[1\) , \( -a - 1\) , \( 1\) , \( -28020 a - 66474\) , \( 4365739 a + 10356761\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrrrrrrrrrr}
1 & 9 & 3 & 6 & 36 & 4 & 12 & 12 & 18 & 2 & 36 & 4 \\
9 & 1 & 3 & 6 & 4 & 36 & 12 & 12 & 2 & 18 & 4 & 36 \\
3 & 3 & 1 & 2 & 12 & 12 & 4 & 4 & 6 & 6 & 12 & 12 \\
6 & 6 & 2 & 1 & 6 & 6 & 2 & 2 & 3 & 3 & 6 & 6 \\
36 & 4 & 12 & 6 & 1 & 36 & 12 & 3 & 2 & 18 & 4 & 9 \\
4 & 36 & 12 & 6 & 36 & 1 & 3 & 12 & 18 & 2 & 9 & 4 \\
12 & 12 & 4 & 2 & 12 & 3 & 1 & 4 & 6 & 6 & 3 & 12 \\
12 & 12 & 4 & 2 & 3 & 12 & 4 & 1 & 6 & 6 & 12 & 3 \\
18 & 2 & 6 & 3 & 2 & 18 & 6 & 6 & 1 & 9 & 2 & 18 \\
2 & 18 & 6 & 3 & 18 & 2 & 6 & 6 & 9 & 1 & 18 & 2 \\
36 & 4 & 12 & 6 & 4 & 9 & 3 & 12 & 2 & 18 & 1 & 36 \\
4 & 36 & 12 & 6 & 9 & 4 & 12 & 3 & 18 & 2 & 36 & 1
\end{array}\right)\)