Elliptic curves in class 676.3-a over \(\Q(\sqrt{3}) \)
Isogeny class 676.3-a contains
8 curves linked by isogenies of
degrees dividing 12.
| Curve label |
Weierstrass Coefficients |
| 676.3-a1
| \( \bigl[0\) , \( -a\) , \( 0\) , \( 1\) , \( 11 a + 17\bigr] \)
|
| 676.3-a2
| \( \bigl[0\) , \( a\) , \( 0\) , \( 1\) , \( -11 a - 17\bigr] \)
|
| 676.3-a3
| \( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( 409 a - 718\) , \( 5865 a - 10165\bigr] \)
|
| 676.3-a4
| \( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( 409 a - 718\) , \( -5866 a + 10163\bigr] \)
|
| 676.3-a5
| \( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( 24 a - 48\) , \( 85 a - 148\bigr] \)
|
| 676.3-a6
| \( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( 24 a - 48\) , \( -86 a + 146\bigr] \)
|
| 676.3-a7
| \( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( 39 a - 118\) , \( -125 a + 325\bigr] \)
|
| 676.3-a8
| \( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( 39 a - 118\) , \( 124 a - 327\bigr] \)
|
Rank: \( 1 \)
\(\left(\begin{array}{rrrrrrrr}
1 & 3 & 4 & 12 & 2 & 6 & 4 & 12 \\
3 & 1 & 12 & 4 & 6 & 2 & 12 & 4 \\
4 & 12 & 1 & 12 & 2 & 6 & 4 & 3 \\
12 & 4 & 12 & 1 & 6 & 2 & 3 & 4 \\
2 & 6 & 2 & 6 & 1 & 3 & 2 & 6 \\
6 & 2 & 6 & 2 & 3 & 1 & 6 & 2 \\
4 & 12 & 4 & 3 & 2 & 6 & 1 & 12 \\
12 & 4 & 3 & 4 & 6 & 2 & 12 & 1
\end{array}\right)\)
