Elliptic curves in class 686.1-d over \(\Q(\sqrt{2}) \)
Isogeny class 686.1-d contains
12 curves linked by isogenies of
degrees dividing 36.
| Curve label |
Weierstrass Coefficients |
| 686.1-d1
| \( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -683 a - 1536\) , \( 19222 a + 21843\bigr] \)
|
| 686.1-d2
| \( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -3 a - 6\) , \( -6 a - 7\bigr] \)
|
| 686.1-d3
| \( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( 17 a + 39\) , \( 126 a + 143\bigr] \)
|
| 686.1-d4
| \( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( 132 a - 376\) , \( -1908 a + 2353\bigr] \)
|
| 686.1-d5
| \( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -143 a - 321\) , \( 1534 a + 1743\bigr] \)
|
| 686.1-d6
| \( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -253 a - 2161\) , \( -5170 a - 37057\bigr] \)
|
| 686.1-d7
| \( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( 37477 a - 93056\) , \( 8696054 a - 9208877\bigr] \)
|
| 686.1-d8
| \( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -43 a - 96\) , \( -270 a - 307\bigr] \)
|
| 686.1-d9
| \( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -2593 a - 4241\) , \( 94830 a + 138943\bigr] \)
|
| 686.1-d10
| \( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -10923 a - 24576\) , \( 1213206 a + 1378643\bigr] \)
|
| 686.1-d11
| \( \bigl[1\) , \( -a + 1\) , \( 1\) , \( 485 a - 759\) , \( -2705 a + 3591\bigr] \)
|
| 686.1-d12
| \( \bigl[1\) , \( -a + 1\) , \( 1\) , \( 103060 a - 164599\) , \( 23909933 a - 32816619\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrrrrrrrrrr}
1 & 9 & 3 & 36 & 6 & 12 & 4 & 18 & 12 & 2 & 36 & 4 \\
9 & 1 & 3 & 4 & 6 & 12 & 36 & 2 & 12 & 18 & 4 & 36 \\
3 & 3 & 1 & 12 & 2 & 4 & 12 & 6 & 4 & 6 & 12 & 12 \\
36 & 4 & 12 & 1 & 6 & 12 & 36 & 2 & 3 & 18 & 4 & 9 \\
6 & 6 & 2 & 6 & 1 & 2 & 6 & 3 & 2 & 3 & 6 & 6 \\
12 & 12 & 4 & 12 & 2 & 1 & 3 & 6 & 4 & 6 & 3 & 12 \\
4 & 36 & 12 & 36 & 6 & 3 & 1 & 18 & 12 & 2 & 9 & 4 \\
18 & 2 & 6 & 2 & 3 & 6 & 18 & 1 & 6 & 9 & 2 & 18 \\
12 & 12 & 4 & 3 & 2 & 4 & 12 & 6 & 1 & 6 & 12 & 3 \\
2 & 18 & 6 & 18 & 3 & 6 & 2 & 9 & 6 & 1 & 18 & 2 \\
36 & 4 & 12 & 4 & 6 & 3 & 9 & 2 & 12 & 18 & 1 & 36 \\
4 & 36 & 12 & 9 & 6 & 12 & 4 & 18 & 3 & 2 & 36 & 1
\end{array}\right)\)
