Elliptic curves in class 500.2-d over \(\Q(\sqrt{6}) \)
Isogeny class 500.2-d contains
8 curves linked by isogenies of
degrees dividing 12.
Curve label |
Weierstrass Coefficients |
500.2-d1
| \( \bigl[a\) , \( -a\) , \( 0\) , \( -22 a - 80\) , \( -746 a - 1918\bigr] \)
|
500.2-d2
| \( \bigl[a\) , \( -a\) , \( a\) , \( 2673 a + 6547\) , \( 732674 a + 1794673\bigr] \)
|
500.2-d3
| \( \bigl[0\) , \( -a\) , \( 0\) , \( 834 a - 2042\) , \( -19846 a + 48613\bigr] \)
|
500.2-d4
| \( \bigl[a\) , \( -a\) , \( a\) , \( 153 a - 383\) , \( 10624 a - 26027\bigr] \)
|
500.2-d5
| \( \bigl[a\) , \( -a\) , \( a\) , \( 328 a - 808\) , \( 5504 a - 13482\bigr] \)
|
500.2-d6
| \( \bigl[a\) , \( -a\) , \( 0\) , \( -57 a - 145\) , \( -358 a - 876\bigr] \)
|
500.2-d7
| \( \bigl[0\) , \( -a\) , \( 0\) , \( -146 a - 362\) , \( 1644 a + 4023\bigr] \)
|
500.2-d8
| \( \bigl[a\) , \( -a\) , \( 0\) , \( -932 a - 2270\) , \( -23858 a - 58376\bigr] \)
|
Rank: \( 1 \)
\(\left(\begin{array}{rrrrrrrr}
1 & 3 & 4 & 12 & 6 & 2 & 12 & 4 \\
3 & 1 & 12 & 4 & 2 & 6 & 4 & 12 \\
4 & 12 & 1 & 12 & 6 & 2 & 3 & 4 \\
12 & 4 & 12 & 1 & 2 & 6 & 4 & 3 \\
6 & 2 & 6 & 2 & 1 & 3 & 2 & 6 \\
2 & 6 & 2 & 6 & 3 & 1 & 6 & 2 \\
12 & 4 & 3 & 4 & 2 & 6 & 1 & 12 \\
4 & 12 & 4 & 3 & 6 & 2 & 12 & 1
\end{array}\right)\)