Elliptic curves in class 49.3-a over 4.4.2624.1
Isogeny class 49.3-a contains
4 curves linked by isogenies of
degrees dividing 6.
| Curve label |
Weierstrass Coefficients |
| 49.3-a1
| \( \bigl[a^{2} - a - 1\) , \( a^{2} - 2 a - 2\) , \( a^{3} - 2 a^{2} - a + 2\) , \( 15 a^{3} - 62 a^{2} + 53 a - 13\) , \( -93 a^{3} + 335 a^{2} - 211 a - 6\bigr] \)
|
| 49.3-a2
| \( \bigl[a^{2} - a - 1\) , \( a^{2} - 2 a - 2\) , \( a^{3} - 2 a^{2} - a + 2\) , \( -2 a^{2} + 3 a + 2\) , \( 2 a^{3} - 7 a^{2} + 2 a + 1\bigr] \)
|
| 49.3-a3
| \( \bigl[a^{3} - 2 a^{2} - 2 a + 1\) , \( -a\) , \( a^{2} - 2 a - 1\) , \( -41 a^{3} + 99 a^{2} + 93 a - 148\) , \( 232 a^{3} - 512 a^{2} - 596 a + 646\bigr] \)
|
| 49.3-a4
| \( \bigl[a^{3} - 2 a^{2} - 2 a + 1\) , \( -a\) , \( a^{2} - 2 a - 1\) , \( -a^{3} + 4 a^{2} - 2 a - 3\) , \( a^{3} - 3 a^{2} + 1\bigr] \)
|
Rank: \( 1 \)
\(\left(\begin{array}{rrrr}
1 & 3 & 2 & 6 \\
3 & 1 & 6 & 2 \\
2 & 6 & 1 & 3 \\
6 & 2 & 3 & 1
\end{array}\right)\)
