Elliptic curves in class 47.1-a over 5.5.70601.1
Isogeny class 47.1-a contains
4 curves linked by isogenies of
degrees dividing 6.
Curve label |
Weierstrass Coefficients |
47.1-a1
| \( \bigl[2 a^{4} - a^{3} - 10 a^{2} + 3\) , \( a^{3} - a^{2} - 3 a + 1\) , \( 2 a^{4} - 2 a^{3} - 9 a^{2} + 4 a + 2\) , \( -3 a^{4} + 8 a^{3} + 3 a^{2} - 7 a - 2\) , \( -6 a^{4} + 17 a^{3} - 10 a\bigr] \)
|
47.1-a2
| \( \bigl[2 a^{4} - 2 a^{3} - 9 a^{2} + 3 a + 3\) , \( a^{4} - 6 a^{2} - a + 3\) , \( a^{4} - 6 a^{2} - 2 a + 4\) , \( 47 a^{4} - 31 a^{3} - 246 a^{2} + 10 a + 150\) , \( -159 a^{4} + 108 a^{3} + 829 a^{2} - 51 a - 493\bigr] \)
|
47.1-a3
| \( \bigl[a\) , \( a^{4} - 7 a^{2} - a + 5\) , \( 0\) , \( -24 a^{4} + 12 a^{3} + 136 a^{2} - 4 a - 84\) , \( -115 a^{4} + 96 a^{3} + 555 a^{2} - 49 a - 327\bigr] \)
|
47.1-a4
| \( \bigl[2 a^{4} - a^{3} - 10 a^{2} + 3\) , \( a^{3} - a^{2} - 3 a + 1\) , \( 2 a^{4} - 2 a^{3} - 9 a^{2} + 4 a + 2\) , \( -3 a^{4} + 8 a^{3} + 8 a^{2} - 12 a - 27\) , \( -6 a^{4} + 18 a^{3} + 12 a^{2} - 25 a - 60\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrr}
1 & 3 & 6 & 2 \\
3 & 1 & 2 & 6 \\
6 & 2 & 1 & 3 \\
2 & 6 & 3 & 1
\end{array}\right)\)