Elliptic curves in class 39.1-f over 4.4.4752.1
Isogeny class 39.1-f contains
4 curves linked by isogenies of
degrees dividing 4.
Curve label |
Weierstrass Coefficients |
39.1-f1
| \( \bigl[a^{2} - a - 2\) , \( -a^{3} + a^{2} + 4 a - 2\) , \( a^{2} - 2\) , \( -1385 a^{3} - 686 a^{2} + 2441 a + 526\) , \( -40165 a^{3} - 19914 a^{2} + 70815 a + 16169\bigr] \)
|
39.1-f2
| \( \bigl[a^{3} - a^{2} - 3 a + 1\) , \( -a\) , \( a^{3} - 3 a - 1\) , \( 3 a^{2} + 16 a - 90\) , \( -23 a^{3} + 128 a^{2} - 125 a - 175\bigr] \)
|
39.1-f3
| \( \bigl[a^{3} - a^{2} - 3 a + 1\) , \( -a\) , \( a^{3} - 3 a - 1\) , \( -7 a^{2} + 31 a - 45\) , \( -5 a^{3} + 39 a^{2} - 113 a + 104\bigr] \)
|
39.1-f4
| \( \bigl[a^{3} - a^{2} - 3 a + 1\) , \( -a\) , \( a^{3} - 3 a - 1\) , \( -2 a^{2} + a\) , \( -2 a^{2} - 2 a + 5\bigr] \)
|
Rank: \( 1 \)
\(\left(\begin{array}{rrrr}
1 & 4 & 2 & 4 \\
4 & 1 & 2 & 4 \\
2 & 2 & 1 & 2 \\
4 & 4 & 2 & 1
\end{array}\right)\)