Elliptic curves in class 39.2-e over 4.4.4752.1
Isogeny class 39.2-e contains
4 curves linked by isogenies of
degrees dividing 14.
| Curve label |
Weierstrass Coefficients |
| 39.2-e1
| \( \bigl[a^{3} - 4 a - 1\) , \( a^{3} - 2 a^{2} - 3 a + 3\) , \( a^{2} - 1\) , \( -3 a^{3} + 4 a^{2} + 9 a - 8\) , \( -2 a^{2} + a + 5\bigr] \)
|
| 39.2-e2
| \( \bigl[a^{2} - a - 1\) , \( -a^{3} + 2 a^{2} + a - 2\) , \( a^{2} - 2\) , \( a^{3} - 7 a^{2} + 5 a + 2\) , \( -a^{3} + 5 a^{2} - 3 a - 2\bigr] \)
|
| 39.2-e3
| \( \bigl[a^{2} - a - 1\) , \( -a^{3} + 2 a^{2} + a - 2\) , \( a^{2} - 2\) , \( 796 a^{3} - 2807 a^{2} + 1735 a + 467\) , \( 34097 a^{3} - 119409 a^{2} + 75770 a + 22634\bigr] \)
|
| 39.2-e4
| \( \bigl[a^{2} - a - 1\) , \( a^{3} - 2 a^{2} - 3 a + 3\) , \( a\) , \( 1365 a^{3} - 4208 a^{2} + 1687 a + 585\) , \( 59243 a^{3} - 199768 a^{2} + 114778 a + 35469\bigr] \)
|
Rank: \( 1 \)
\(\left(\begin{array}{rrrr}
1 & 2 & 14 & 7 \\
2 & 1 & 7 & 14 \\
14 & 7 & 1 & 2 \\
7 & 14 & 2 & 1
\end{array}\right)\)
