Elliptic curves in class 8.1-d over 4.4.16448.1
Isogeny class 8.1-d contains
4 curves linked by isogenies of
degrees dividing 4.
| Curve label |
Weierstrass Coefficients |
| 8.1-d1
| \( \bigl[a^{3} - 2 a^{2} - 5 a\) , \( a^{3} - 3 a^{2} - 2 a + 3\) , \( 0\) , \( 398 a^{3} - 1378 a^{2} - 370 a + 547\) , \( -8934 a^{3} + 30936 a^{2} + 8355 a - 12216\bigr] \)
|
| 8.1-d2
| \( \bigl[0\) , \( a^{2} - a - 4\) , \( a\) , \( -a^{2} + 2 a + 5\) , \( -a - 2\bigr] \)
|
| 8.1-d3
| \( \bigl[2 a^{3} - 5 a^{2} - 8 a + 2\) , \( a^{2} - 2 a - 2\) , \( 2 a^{3} - 5 a^{2} - 8 a + 2\) , \( 3 a^{3} + a^{2} - 32 a - 34\) , \( -17 a^{3} + 29 a^{2} + 106 a + 44\bigr] \)
|
| 8.1-d4
| \( \bigl[a^{3} - 3 a^{2} - 3 a + 2\) , \( a^{3} - 2 a^{2} - 4 a\) , \( 2 a^{3} - 5 a^{2} - 7 a + 2\) , \( -2 a^{3} + 18 a^{2} - 27 a - 30\) , \( -9 a^{3} - 5 a^{2} + 114 a + 76\bigr] \)
|
Rank: \( 1 \)
\(\left(\begin{array}{rrrr}
1 & 4 & 2 & 4 \\
4 & 1 & 2 & 4 \\
2 & 2 & 1 & 2 \\
4 & 4 & 2 & 1
\end{array}\right)\)
