Elliptic curves in class 41.1-b over 6.6.485125.1
Isogeny class 41.1-b contains
4 curves linked by isogenies of
degrees dividing 6.
| Curve label |
Weierstrass Coefficients |
| 41.1-b1
| \( \bigl[a^{5} - 5 a^{3} + 4 a + 1\) , \( -2 a^{5} + 3 a^{4} + 8 a^{3} - 9 a^{2} - 5 a + 2\) , \( a^{3} - 2 a - 1\) , \( -2 a^{5} + 3 a^{4} + 7 a^{3} - 4 a^{2} - 8 a + 3\) , \( -a^{5} + 3 a^{4} + 2 a^{3} - 5 a^{2} - a\bigr] \)
|
| 41.1-b2
| \( \bigl[a^{3} - 2 a\) , \( -a^{5} + 2 a^{4} + 5 a^{3} - 7 a^{2} - 7 a + 2\) , \( a^{5} - 5 a^{3} + 5 a\) , \( -2 a^{5} + a^{4} + 9 a^{3} - a^{2} - 9 a - 2\) , \( -44 a^{5} + 82 a^{4} + 189 a^{3} - 329 a^{2} - 145 a + 209\bigr] \)
|
| 41.1-b3
| \( \bigl[-a^{5} + 2 a^{4} + 4 a^{3} - 6 a^{2} - 3 a + 2\) , \( a^{5} - a^{4} - 5 a^{3} + 4 a^{2} + 5 a - 2\) , \( -a^{5} + 2 a^{4} + 4 a^{3} - 7 a^{2} - 2 a + 3\) , \( 7 a^{5} + a^{4} - 46 a^{3} + 59 a - 26\) , \( 18 a^{5} - 20 a^{4} - 50 a^{3} + 53 a^{2} - 44 a + 23\bigr] \)
|
| 41.1-b4
| \( \bigl[a^{5} - 5 a^{3} + 4 a + 1\) , \( -2 a^{5} + 3 a^{4} + 8 a^{3} - 9 a^{2} - 5 a + 2\) , \( a^{3} - 2 a - 1\) , \( -22 a^{5} + 28 a^{4} + 107 a^{3} - 89 a^{2} - 118 a + 18\) , \( -82 a^{5} + 112 a^{4} + 399 a^{3} - 397 a^{2} - 420 a + 138\bigr] \)
|
Rank: \( 1 \)
\(\left(\begin{array}{rrrr}
1 & 3 & 6 & 2 \\
3 & 1 & 2 & 6 \\
6 & 2 & 1 & 3 \\
2 & 6 & 3 & 1
\end{array}\right)\)
