Elliptic curves in class 12544.2-e over \(\Q(\sqrt{-3}) \)
Isogeny class 12544.2-e contains
8 curves linked by isogenies of
degrees dividing 12.
Curve label |
Weierstrass Coefficients |
12544.2-e1
| \( \bigl[0\) , \( a + 1\) , \( 0\) , \( 88 a - 1624\) , \( -2480 a + 24592\bigr] \)
|
12544.2-e2
| \( \bigl[0\) , \( a + 1\) , \( 0\) , \( 74 a + 63\) , \( -359 a - 1441\bigr] \)
|
12544.2-e3
| \( \bigl[0\) , \( a + 1\) , \( 0\) , \( -72 a + 136\) , \( -432 a + 1936\bigr] \)
|
12544.2-e4
| \( \bigl[0\) , \( a + 1\) , \( 0\) , \( -6 a - 17\) , \( 9 a + 15\bigr] \)
|
12544.2-e5
| \( \bigl[0\) , \( a + 1\) , \( 0\) , \( 8 a - 104\) , \( -48 a + 336\bigr] \)
|
12544.2-e6
| \( \bigl[0\) , \( a + 1\) , \( 0\) , \( 8 a - 24\) , \( 16 a - 48\bigr] \)
|
12544.2-e7
| \( \bigl[0\) , \( a + 1\) , \( 0\) , \( -6 a - 97\) , \( -55 a - 385\bigr] \)
|
12544.2-e8
| \( \bigl[0\) , \( a + 1\) , \( 0\) , \( -86 a - 1537\) , \( -2567 a - 23649\bigr] \)
|
Rank: \( 1 \)
\(\left(\begin{array}{rrrrrrrr}
1 & 3 & 4 & 12 & 2 & 4 & 6 & 12 \\
3 & 1 & 12 & 4 & 6 & 12 & 2 & 4 \\
4 & 12 & 1 & 12 & 2 & 4 & 6 & 3 \\
12 & 4 & 12 & 1 & 6 & 3 & 2 & 4 \\
2 & 6 & 2 & 6 & 1 & 2 & 3 & 6 \\
4 & 12 & 4 & 3 & 2 & 1 & 6 & 12 \\
6 & 2 & 6 & 2 & 3 & 6 & 1 & 2 \\
12 & 4 & 3 & 4 & 6 & 12 & 2 & 1
\end{array}\right)\)