Elliptic curves in class 686.2-d over \(\Q(\sqrt{2}) \)
Isogeny class 686.2-d contains
12 curves linked by isogenies of
degrees dividing 36.
| Curve label |
Weierstrass Coefficients |
| 686.2-d1
| \( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( 681 a - 1536\) , \( -19223 a + 21843\bigr] \)
|
| 686.2-d2
| \( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( a - 6\) , \( 5 a - 7\bigr] \)
|
| 686.2-d3
| \( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -19 a + 39\) , \( -127 a + 143\bigr] \)
|
| 686.2-d4
| \( \bigl[1\) , \( a + 1\) , \( 1\) , \( -485 a - 759\) , \( 2705 a + 3591\bigr] \)
|
| 686.2-d5
| \( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( 141 a - 321\) , \( -1535 a + 1743\bigr] \)
|
| 686.2-d6
| \( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( 2591 a - 4241\) , \( -94831 a + 138943\bigr] \)
|
| 686.2-d7
| \( \bigl[1\) , \( a + 1\) , \( 1\) , \( -103060 a - 164599\) , \( -23909933 a - 32816619\bigr] \)
|
| 686.2-d8
| \( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( 41 a - 96\) , \( 269 a - 307\bigr] \)
|
| 686.2-d9
| \( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( 251 a - 2161\) , \( 5169 a - 37057\bigr] \)
|
| 686.2-d10
| \( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( 10921 a - 24576\) , \( -1213207 a + 1378643\bigr] \)
|
| 686.2-d11
| \( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -134 a - 376\) , \( 1907 a + 2353\bigr] \)
|
| 686.2-d12
| \( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -37479 a - 93056\) , \( -8696055 a - 9208877\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrrrrrrrrrr}
1 & 9 & 3 & 36 & 6 & 12 & 4 & 18 & 12 & 2 & 36 & 4 \\
9 & 1 & 3 & 4 & 6 & 12 & 36 & 2 & 12 & 18 & 4 & 36 \\
3 & 3 & 1 & 12 & 2 & 4 & 12 & 6 & 4 & 6 & 12 & 12 \\
36 & 4 & 12 & 1 & 6 & 12 & 36 & 2 & 3 & 18 & 4 & 9 \\
6 & 6 & 2 & 6 & 1 & 2 & 6 & 3 & 2 & 3 & 6 & 6 \\
12 & 12 & 4 & 12 & 2 & 1 & 3 & 6 & 4 & 6 & 3 & 12 \\
4 & 36 & 12 & 36 & 6 & 3 & 1 & 18 & 12 & 2 & 9 & 4 \\
18 & 2 & 6 & 2 & 3 & 6 & 18 & 1 & 6 & 9 & 2 & 18 \\
12 & 12 & 4 & 3 & 2 & 4 & 12 & 6 & 1 & 6 & 12 & 3 \\
2 & 18 & 6 & 18 & 3 & 6 & 2 & 9 & 6 & 1 & 18 & 2 \\
36 & 4 & 12 & 4 & 6 & 3 & 9 & 2 & 12 & 18 & 1 & 36 \\
4 & 36 & 12 & 9 & 6 & 12 & 4 & 18 & 3 & 2 & 36 & 1
\end{array}\right)\)
