Elliptic curves in class 39.1-a over 4.4.4752.1
Isogeny class 39.1-a contains
4 curves linked by isogenies of
degrees dividing 4.
Curve label |
Weierstrass Coefficients |
39.1-a1
| \( \bigl[a^{3} - 4 a\) , \( -a^{2} + 2\) , \( a^{3} - a^{2} - 2 a + 1\) , \( -a^{3} + 4 a^{2} + 19 a - 89\) , \( 22 a^{3} - 125 a^{2} + 144 a + 85\bigr] \)
|
39.1-a2
| \( \bigl[a^{3} - 4 a\) , \( -a^{2} + 2\) , \( a^{3} - a^{2} - 2 a + 1\) , \( -a^{3} - 6 a^{2} + 34 a - 44\) , \( 4 a^{3} - 46 a^{2} + 147 a - 149\bigr] \)
|
39.1-a3
| \( \bigl[a^{3} - 4 a\) , \( -a^{2} + 2\) , \( a^{3} - a^{2} - 2 a + 1\) , \( -a^{3} - a^{2} + 4 a + 1\) , \( -a^{3} + 6 a - 5\bigr] \)
|
39.1-a4
| \( \bigl[1\) , \( a^{3} - a^{2} - 4 a + 1\) , \( a^{3} - a^{2} - 2 a + 1\) , \( -1385 a^{3} - 686 a^{2} + 2441 a + 527\) , \( 40164 a^{3} + 19914 a^{2} - 70813 a - 16170\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrr}
1 & 2 & 4 & 4 \\
2 & 1 & 2 & 2 \\
4 & 2 & 1 & 4 \\
4 & 2 & 4 & 1
\end{array}\right)\)