Elliptic curves in class 27648.2-n over \(\Q(\sqrt{-2}) \)
Isogeny class 27648.2-n contains
8 curves linked by isogenies of
degrees dividing 12.
Curve label |
Weierstrass Coefficients |
27648.2-n1
| \( \bigl[0\) , \( a + 1\) , \( 0\) , \( 470 a - 37\) , \( 3705 a + 3939\bigr] \)
|
27648.2-n2
| \( \bigl[0\) , \( a + 1\) , \( 0\) , \( 382 a - 389\) , \( -4615 a + 611\bigr] \)
|
27648.2-n3
| \( \bigl[0\) , \( a + 1\) , \( 0\) , \( 10 a + 13\) , \( 17 a - 31\bigr] \)
|
27648.2-n4
| \( \bigl[0\) , \( a + 1\) , \( 0\) , \( 2 a - 19\) , \( -3 a - 39\bigr] \)
|
27648.2-n5
| \( \bigl[0\) , \( a + 1\) , \( 0\) , \( 22 a - 29\) , \( -79 a - 37\bigr] \)
|
27648.2-n6
| \( \bigl[0\) , \( a + 1\) , \( 0\) , \( 30 a + 3\) , \( 81 a + 27\bigr] \)
|
27648.2-n7
| \( \bigl[0\) , \( a + 1\) , \( 0\) , \( -90 a - 117\) , \( 393 a + 627\bigr] \)
|
27648.2-n8
| \( \bigl[0\) , \( a + 1\) , \( 0\) , \( -18 a + 171\) , \( -567 a + 243\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrrrrrr}
1 & 12 & 4 & 12 & 6 & 2 & 4 & 3 \\
12 & 1 & 12 & 4 & 2 & 6 & 3 & 4 \\
4 & 12 & 1 & 3 & 6 & 2 & 4 & 12 \\
12 & 4 & 3 & 1 & 2 & 6 & 12 & 4 \\
6 & 2 & 6 & 2 & 1 & 3 & 6 & 2 \\
2 & 6 & 2 & 6 & 3 & 1 & 2 & 6 \\
4 & 3 & 4 & 12 & 6 & 2 & 1 & 12 \\
3 & 4 & 12 & 4 & 2 & 6 & 12 & 1
\end{array}\right)\)