Elliptic curves in class 14.1-a over 4.4.10889.1
Isogeny class 14.1-a contains
6 curves linked by isogenies of
degrees dividing 8.
| Curve label |
Weierstrass Coefficients |
| 14.1-a1
| \( \bigl[a^{3} - 6 a\) , \( -a^{3} + a^{2} + 4 a - 2\) , \( a^{3} - a^{2} - 4 a + 2\) , \( -20 a^{3} + 16 a^{2} + 127 a - 92\) , \( -43 a^{3} - 20 a^{2} + 457 a - 309\bigr] \)
|
| 14.1-a2
| \( \bigl[a^{3} - 6 a\) , \( -a^{3} + a^{2} + 4 a - 2\) , \( a^{3} - a^{2} - 4 a + 2\) , \( -5 a^{3} + 6 a^{2} + 22 a - 12\) , \( 6 a^{3} - 10 a^{2} - 22 a + 19\bigr] \)
|
| 14.1-a3
| \( \bigl[a^{3} - 6 a\) , \( -a^{3} + a^{2} + 4 a - 2\) , \( a^{3} - a^{2} - 4 a + 2\) , \( 120 a^{3} - 349 a^{2} + 77 a + 63\) , \( 2081 a^{3} - 6717 a^{2} + 3463 a + 42\bigr] \)
|
| 14.1-a4
| \( \bigl[a^{3} - 6 a\) , \( a^{3} - a^{2} - 5 a + 1\) , \( a^{3} - a^{2} - 5 a + 3\) , \( a^{3} - 6 a - 2\) , \( 27 a^{3} - 8 a^{2} - 142 a - 44\bigr] \)
|
| 14.1-a5
| \( \bigl[a\) , \( -a + 1\) , \( a^{3} - 5 a\) , \( 3 a^{3} - 21 a - 6\) , \( -2 a^{3} + a^{2} + 9 a + 2\bigr] \)
|
| 14.1-a6
| \( \bigl[a^{3} - a^{2} - 4 a + 3\) , \( a^{2} - 3\) , \( a^{2} - a - 2\) , \( 98 a^{3} - 287 a^{2} + 54 a + 32\) , \( 2311 a^{3} - 6868 a^{2} + 1761 a + 1157\bigr] \)
|
Rank: \( 1 \)
\(\left(\begin{array}{rrrrrr}
1 & 2 & 2 & 4 & 4 & 2 \\
2 & 1 & 4 & 2 & 2 & 4 \\
2 & 4 & 1 & 8 & 8 & 4 \\
4 & 2 & 8 & 1 & 4 & 8 \\
4 & 2 & 8 & 4 & 1 & 8 \\
2 & 4 & 4 & 8 & 8 & 1
\end{array}\right)\)
