Elliptic curves in class 47.1-b over 6.6.592661.1
Isogeny class 47.1-b contains
4 curves linked by isogenies of
degrees dividing 6.
| Curve label |
Weierstrass Coefficients |
| 47.1-b1
| \( \bigl[a^{5} - 4 a^{3} + a^{2} + 2 a - 2\) , \( a^{5} - 5 a^{3} + a^{2} + 5 a - 2\) , \( a^{5} - a^{4} - 4 a^{3} + 4 a^{2} + 2 a - 2\) , \( 767 a^{5} - 1165 a^{4} - 3414 a^{3} + 4728 a^{2} + 2262 a - 2760\) , \( 16792 a^{5} - 23007 a^{4} - 75423 a^{3} + 94591 a^{2} + 51674 a - 53458\bigr] \)
|
| 47.1-b2
| \( \bigl[a^{5} - 4 a^{3} + a^{2} + a - 3\) , \( a^{5} - 4 a^{3} + 2 a - 1\) , \( a^{5} - a^{4} - 5 a^{3} + 4 a^{2} + 4 a - 2\) , \( 6 a^{5} - 3 a^{4} - 26 a^{3} + 16 a^{2} + 21 a - 9\) , \( -a^{5} + 4 a^{4} + 8 a^{3} - 11 a^{2} - 8 a + 2\bigr] \)
|
| 47.1-b3
| \( \bigl[a^{5} - 4 a^{3} + a^{2} + a - 3\) , \( a^{5} - 4 a^{3} + 2 a - 1\) , \( a^{5} - a^{4} - 5 a^{3} + 4 a^{2} + 4 a - 2\) , \( a^{5} - 3 a^{4} - 6 a^{3} + 31 a^{2} + 16 a - 59\) , \( 4 a^{5} - 18 a^{4} - 24 a^{3} + 118 a^{2} + 43 a - 176\bigr] \)
|
| 47.1-b4
| \( \bigl[a^{5} - a^{4} - 5 a^{3} + 4 a^{2} + 5 a - 1\) , \( a^{5} - 2 a^{4} - 4 a^{3} + 9 a^{2} - 4\) , \( a^{5} - a^{4} - 5 a^{3} + 5 a^{2} + 4 a - 3\) , \( -19 a^{5} + 38 a^{4} + 85 a^{3} - 167 a^{2} - 8 a + 12\) , \( -105 a^{5} + 197 a^{4} + 473 a^{3} - 942 a^{2} + 53 a + 129\bigr] \)
|
Rank: \( 1 \)
\(\left(\begin{array}{rrrr}
1 & 6 & 3 & 2 \\
6 & 1 & 2 & 3 \\
3 & 2 & 1 & 6 \\
2 & 3 & 6 & 1
\end{array}\right)\)
