Elliptic curves in class 27648.3-bp over \(\Q(\sqrt{-2}) \)
Isogeny class 27648.3-bp contains
8 curves linked by isogenies of
degrees dividing 16.
Curve label |
Weierstrass Coefficients |
27648.3-bp1
| \( \bigl[0\) , \( a - 1\) , \( 0\) , \( 62 a + 31\) , \( 1737 a - 751\bigr] \)
|
27648.3-bp2
| \( \bigl[0\) , \( a - 1\) , \( 0\) , \( 2 a + 1\) , \( -3 a - 1\bigr] \)
|
27648.3-bp3
| \( \bigl[0\) , \( a - 1\) , \( 0\) , \( -18 a - 9\) , \( -23 a + 25\bigr] \)
|
27648.3-bp4
| \( \bigl[0\) , \( a - 1\) , \( 0\) , \( -98 a - 49\) , \( 457 a - 95\bigr] \)
|
27648.3-bp5
| \( \bigl[0\) , \( a - 1\) , \( 0\) , \( 1902 a - 1569\) , \( 45913 a - 623\bigr] \)
|
27648.3-bp6
| \( \bigl[0\) , \( a - 1\) , \( 0\) , \( 782 a + 2911\) , \( 40761 a - 36463\bigr] \)
|
27648.3-bp7
| \( \bigl[0\) , \( a - 1\) , \( 0\) , \( -258 a - 129\) , \( -1943 a + 1009\bigr] \)
|
27648.3-bp8
| \( \bigl[0\) , \( a - 1\) , \( 0\) , \( -1538 a - 769\) , \( 29257 a - 10319\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrrrrrr}
1 & 8 & 4 & 2 & 2 & 2 & 8 & 4 \\
8 & 1 & 2 & 4 & 16 & 16 & 4 & 8 \\
4 & 2 & 1 & 2 & 8 & 8 & 2 & 4 \\
2 & 4 & 2 & 1 & 4 & 4 & 4 & 2 \\
2 & 16 & 8 & 4 & 1 & 4 & 16 & 8 \\
2 & 16 & 8 & 4 & 4 & 1 & 16 & 8 \\
8 & 4 & 2 & 4 & 16 & 16 & 1 & 8 \\
4 & 8 & 4 & 2 & 8 & 8 & 8 & 1
\end{array}\right)\)