Elliptic curves in class 31212.4-f over \(\Q(\sqrt{-2}) \)
Isogeny class 31212.4-f contains
8 curves linked by isogenies of
degrees dividing 12.
| Curve label |
Weierstrass Coefficients |
| 31212.4-f1
| \( \bigl[a\) , \( -a + 1\) , \( a\) , \( -114 a - 1403\) , \( 2909 a + 19833\bigr] \)
|
| 31212.4-f2
| \( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -631 a - 1096\) , \( -12094 a - 11213\bigr] \)
|
| 31212.4-f3
| \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 76 a - 119\) , \( -491 a + 430\bigr] \)
|
| 31212.4-f4
| \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -112 a - 7\) , \( -369 a + 468\bigr] \)
|
| 31212.4-f5
| \( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -46 a - 61\) , \( -151 a - 287\bigr] \)
|
| 31212.4-f6
| \( \bigl[a\) , \( -a + 1\) , \( a\) , \( a - 88\) , \( 132 a + 292\bigr] \)
|
| 31212.4-f7
| \( \bigl[a\) , \( -a + 1\) , \( a\) , \( -164 a + 287\) , \( 123 a + 2677\bigr] \)
|
| 31212.4-f8
| \( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 259 a + 34\) , \( -1680 a - 1147\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrrrrrr}
1 & 12 & 4 & 12 & 6 & 2 & 4 & 3 \\
12 & 1 & 12 & 4 & 2 & 6 & 3 & 4 \\
4 & 12 & 1 & 3 & 6 & 2 & 4 & 12 \\
12 & 4 & 3 & 1 & 2 & 6 & 12 & 4 \\
6 & 2 & 6 & 2 & 1 & 3 & 6 & 2 \\
2 & 6 & 2 & 6 & 3 & 1 & 2 & 6 \\
4 & 3 & 4 & 12 & 6 & 2 & 1 & 12 \\
3 & 4 & 12 & 4 & 2 & 6 & 12 & 1
\end{array}\right)\)
