Elliptic curves in class 49.4-a over 4.4.2624.1
Isogeny class 49.4-a contains
4 curves linked by isogenies of
degrees dividing 6.
| Curve label |
Weierstrass Coefficients |
| 49.4-a1
| \( \bigl[a^{3} - a^{2} - 3 a\) , \( a^{3} - a^{2} - 4 a + 1\) , \( a\) , \( 38 a^{3} - 41 a^{2} - 159 a - 66\) , \( -241 a^{3} + 276 a^{2} + 974 a + 319\bigr] \)
|
| 49.4-a2
| \( \bigl[a^{3} - a^{2} - 3 a\) , \( a^{3} - a^{2} - 4 a + 1\) , \( a\) , \( 3 a^{3} - a^{2} - 9 a - 1\) , \( 3 a^{3} - 7 a - 2\bigr] \)
|
| 49.4-a3
| \( \bigl[a^{3} - 2 a^{2} - 2 a + 1\) , \( -a^{3} + 2 a^{2} + 3 a - 2\) , \( a^{2} - 2 a\) , \( 4 a^{3} - 24 a^{2} - 22 a - 8\) , \( 4 a^{3} + 39 a^{2} + 126 a + 47\bigr] \)
|
| 49.4-a4
| \( \bigl[a^{3} - 2 a^{2} - 2 a + 1\) , \( -a^{3} + 2 a^{2} + 3 a - 2\) , \( a^{2} - 2 a\) , \( -a^{3} + a^{2} + 3 a + 2\) , \( a^{3} - 2 a^{2} - 2 a - 1\bigr] \)
|
Rank: \( 1 \)
\(\left(\begin{array}{rrrr}
1 & 3 & 2 & 6 \\
3 & 1 & 6 & 2 \\
2 & 6 & 1 & 3 \\
6 & 2 & 3 & 1
\end{array}\right)\)
