Elliptic curves in class 16.4-b over 4.4.9248.1
Isogeny class 16.4-b contains
8 curves linked by isogenies of
degrees dividing 16.
| Curve label |
Weierstrass Coefficients |
| 16.4-b1
| \( \bigl[a^{2} - 2\) , \( -1\) , \( a^{2} - 2\) , \( -a^{2} - 1\) , \( -6 a^{2} + 2\bigr] \)
|
| 16.4-b2
| \( \bigl[a\) , \( a^{2} - 2\) , \( a\) , \( 4 a^{2} - 16\) , \( 3 a^{2} - 13\bigr] \)
|
| 16.4-b3
| \( \bigl[a\) , \( a^{2} - 2\) , \( a\) , \( -6 a^{2} + 29\) , \( 28 a^{2} - 128\bigr] \)
|
| 16.4-b4
| \( \bigl[a\) , \( -a^{2} + 2\) , \( a\) , \( -15 a^{3} - 46 a^{2} - 20 a + 1\) , \( 166 a^{3} + 392 a^{2} - 22 a - 138\bigr] \)
|
| 16.4-b5
| \( \bigl[a\) , \( -a^{2} + 2\) , \( a\) , \( -6 a^{2} + 1\) , \( 14 a^{2} - 6\bigr] \)
|
| 16.4-b6
| \( \bigl[a\) , \( -a^{2} + 2\) , \( a\) , \( -a^{2} + 1\) , \( 0\bigr] \)
|
| 16.4-b7
| \( \bigl[a\) , \( -a^{2} + 2\) , \( a\) , \( 15 a^{3} - 46 a^{2} + 20 a + 1\) , \( -166 a^{3} + 392 a^{2} + 22 a - 138\bigr] \)
|
| 16.4-b8
| \( \bigl[a\) , \( -a^{2} + 4\) , \( a\) , \( -2 a^{2} + 7\) , \( -2 a^{2} + 8\bigr] \)
|
Rank: \( 1 \)
\(\left(\begin{array}{rrrrrrrr}
1 & 2 & 4 & 16 & 8 & 4 & 16 & 8 \\
2 & 1 & 2 & 8 & 4 & 2 & 8 & 4 \\
4 & 2 & 1 & 16 & 8 & 4 & 16 & 8 \\
16 & 8 & 16 & 1 & 2 & 4 & 4 & 8 \\
8 & 4 & 8 & 2 & 1 & 2 & 2 & 4 \\
4 & 2 & 4 & 4 & 2 & 1 & 4 & 2 \\
16 & 8 & 16 & 4 & 2 & 4 & 1 & 8 \\
8 & 4 & 8 & 8 & 4 & 2 & 8 & 1
\end{array}\right)\)
