Elliptic curves in class 47.1-a over 6.6.592661.1
Isogeny class 47.1-a contains
4 curves linked by isogenies of
degrees dividing 4.
| Curve label |
Weierstrass Coefficients |
| 47.1-a1
| \( \bigl[a^{5} - 4 a^{3} + a^{2} + a - 2\) , \( -a^{4} + 5 a^{2} - 3\) , \( 2 a^{5} - a^{4} - 9 a^{3} + 4 a^{2} + 6 a - 2\) , \( -60 a^{5} + 84 a^{4} + 210 a^{3} - 318 a^{2} + 13 a + 37\) , \( -358 a^{5} + 547 a^{4} + 1214 a^{3} - 2098 a^{2} + 208 a + 319\bigr] \)
|
| 47.1-a2
| \( \bigl[a^{5} - a^{4} - 5 a^{3} + 4 a^{2} + 5 a - 2\) , \( -a^{4} + 5 a^{2} - 4\) , \( 2 a^{5} - 2 a^{4} - 9 a^{3} + 8 a^{2} + 5 a - 3\) , \( a^{5} - a^{4} - 5 a^{3} + 5 a^{2} + 5 a - 4\) , \( 16 a^{5} + 17 a^{4} - 47 a^{3} - 31 a^{2} + 23 a + 6\bigr] \)
|
| 47.1-a3
| \( \bigl[a^{2} - 2\) , \( -a^{5} + 2 a^{4} + 5 a^{3} - 9 a^{2} - 4 a + 4\) , \( a^{5} - 4 a^{3} + a^{2} + a - 3\) , \( -640 a^{5} + 216 a^{4} + 3345 a^{3} - 347 a^{2} - 3444 a - 992\) , \( 4631 a^{5} - 1611 a^{4} - 24188 a^{3} + 2739 a^{2} + 24854 a + 6981\bigr] \)
|
| 47.1-a4
| \( \bigl[a + 1\) , \( -2 a^{5} + 3 a^{4} + 9 a^{3} - 11 a^{2} - 6 a + 3\) , \( a^{5} - a^{4} - 4 a^{3} + 4 a^{2} + a - 1\) , \( 21 a^{5} - 24 a^{4} - 64 a^{3} + 75 a^{2} - 9 a - 80\) , \( 258 a^{5} - 185 a^{4} - 1121 a^{3} + 481 a^{2} + 835 a - 133\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrr}
1 & 4 & 2 & 4 \\
4 & 1 & 2 & 4 \\
2 & 2 & 1 & 2 \\
4 & 4 & 2 & 1
\end{array}\right)\)
