Elliptic curves in class 41.2-a over 4.4.17725.1
Isogeny class 41.2-a contains
4 curves linked by isogenies of
degrees dividing 6.
| Curve label |
Weierstrass Coefficients |
| 41.2-a1
| \( \bigl[a^{3} - 7 a - 6\) , \( -a^{3} + a^{2} + 7 a\) , \( a^{2} - a - 7\) , \( -10 a^{3} + 35 a^{2} + 51 a - 188\) , \( 17 a^{3} - 121 a^{2} - 48 a + 741\bigr] \)
|
| 41.2-a2
| \( \bigl[a^{3} - 7 a - 6\) , \( -a^{3} + a^{2} + 7 a\) , \( a^{2} - a - 7\) , \( 30 a^{3} - 120 a^{2} - 139 a + 687\) , \( 97 a^{3} - 428 a^{2} - 430 a + 2471\bigr] \)
|
| 41.2-a3
| \( \bigl[a^{3} - a^{2} - 6 a + 1\) , \( a^{3} - 2 a^{2} - 5 a + 8\) , \( a^{3} - a^{2} - 7 a\) , \( 7 a^{3} + 5 a^{2} - 51 a - 63\) , \( 12 a^{3} + 14 a^{2} - 92 a - 142\bigr] \)
|
| 41.2-a4
| \( \bigl[a^{3} - a^{2} - 6 a + 1\) , \( a^{3} - 2 a^{2} - 5 a + 8\) , \( a^{3} - a^{2} - 7 a\) , \( 12 a^{3} - 15 a^{2} - 66 a + 12\) , \( 23 a^{3} - 41 a^{2} - 113 a + 84\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrr}
1 & 2 & 3 & 6 \\
2 & 1 & 6 & 3 \\
3 & 6 & 1 & 2 \\
6 & 3 & 2 & 1
\end{array}\right)\)
