Elliptic curves in class 49.1-a over 4.4.1957.1
Isogeny class 49.1-a contains
4 curves linked by isogenies of
degrees dividing 6.
| Curve label |
Weierstrass Coefficients |
| 49.1-a1
| \( \bigl[a^{2} - 2\) , \( -a^{3} + a^{2} + 4 a - 1\) , \( a\) , \( -30 a^{3} + 55 a^{2} + 22 a - 15\) , \( -267 a^{3} + 469 a^{2} + 242 a - 153\bigr] \)
|
| 49.1-a2
| \( \bigl[a^{2} - 2\) , \( -a^{2} + a + 3\) , \( a^{3} - 4 a - 1\) , \( -63 a^{3} + 23 a^{2} + 227 a - 17\) , \( 162 a^{3} - 125 a^{2} - 566 a + 280\bigr] \)
|
| 49.1-a3
| \( \bigl[a^{3} - 4 a\) , \( a^{3} - 3 a\) , \( a^{2} - a - 1\) , \( a^{3} - a^{2} - 3 a\) , \( a^{3} - a\bigr] \)
|
| 49.1-a4
| \( \bigl[a\) , \( -a^{3} + 3 a + 1\) , \( -a^{3} + a^{2} + 4 a\) , \( -a^{3} - 16 a^{2} + 56 a - 44\) , \( -109 a^{3} + 141 a^{2} + 199 a - 57\bigr] \)
|
Rank: \( 1 \)
\(\left(\begin{array}{rrrr}
1 & 6 & 3 & 2 \\
6 & 1 & 2 & 3 \\
3 & 2 & 1 & 6 \\
2 & 3 & 6 & 1
\end{array}\right)\)
