Elliptic curves in class 768.1-e over \(\Q(\sqrt{3}) \)
Isogeny class 768.1-e contains
8 curves linked by isogenies of
degrees dividing 16.
| Curve label |
Weierstrass Coefficients |
| 768.1-e1
| \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 4138 a - 7169\) , \( 191739 a - 332103\bigr] \)
|
| 768.1-e2
| \( \bigl[0\) , \( a - 1\) , \( 0\) , \( 62 a + 111\) , \( 2637 a + 4569\bigr] \)
|
| 768.1-e3
| \( \bigl[0\) , \( -1\) , \( 0\) , \( -520 a + 901\) , \( 10685 a - 18507\bigr] \)
|
| 768.1-e4
| \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 18 a - 29\) , \( 43 a - 75\bigr] \)
|
| 768.1-e5
| \( \bigl[0\) , \( a - 1\) , \( 0\) , \( -98 a - 169\) , \( 637 a + 1105\bigr] \)
|
| 768.1-e6
| \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 258 a - 449\) , \( 3043 a - 5271\bigr] \)
|
| 768.1-e7
| \( \bigl[0\) , \( a - 1\) , \( 0\) , \( -1538 a - 2689\) , \( 43117 a + 74761\bigr] \)
|
| 768.1-e8
| \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 218 a - 449\) , \( 3467 a - 6183\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrrrrrr}
1 & 16 & 8 & 4 & 8 & 2 & 16 & 4 \\
16 & 1 & 8 & 4 & 2 & 8 & 4 & 16 \\
8 & 8 & 1 & 2 & 4 & 4 & 8 & 8 \\
4 & 4 & 2 & 1 & 2 & 2 & 4 & 4 \\
8 & 2 & 4 & 2 & 1 & 4 & 2 & 8 \\
2 & 8 & 4 & 2 & 4 & 1 & 8 & 2 \\
16 & 4 & 8 & 4 & 2 & 8 & 1 & 16 \\
4 & 16 & 8 & 4 & 8 & 2 & 16 & 1
\end{array}\right)\)
