Elliptic curves in class 47.1-a over 4.4.1957.1
Isogeny class 47.1-a contains
4 curves linked by isogenies of
degrees dividing 6.
Curve label |
Weierstrass Coefficients |
47.1-a1
| \( \bigl[a^{2} - 2\) , \( a\) , \( a^{2} - a - 2\) , \( -a^{2} + 3 a\) , \( 64 a^{3} + 28 a^{2} - 249 a - 166\bigr] \)
|
47.1-a2
| \( \bigl[a^{2} - a - 1\) , \( -2 a^{3} + a^{2} + 8 a\) , \( -a^{3} + a^{2} + 4 a - 1\) , \( 7 a^{3} - 3 a^{2} - 21 a - 4\) , \( -5 a^{3} + 2 a^{2} + 15 a + 2\bigr] \)
|
47.1-a3
| \( \bigl[a^{2} - a - 1\) , \( -2 a^{3} + a^{2} + 8 a\) , \( -a^{3} + a^{2} + 4 a - 1\) , \( 32 a^{3} - 58 a^{2} - 26 a + 21\) , \( -197 a^{3} + 305 a^{2} + 233 a - 53\bigr] \)
|
47.1-a4
| \( \bigl[a^{3} - 4 a\) , \( -2 a^{3} + a^{2} + 7 a - 1\) , \( a^{3} - 4 a - 1\) , \( 2 a^{3} - 3 a^{2} - 4 a + 1\) , \( 2 a^{3} - 3 a^{2} - 2 a - 1\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrr}
1 & 6 & 3 & 2 \\
6 & 1 & 2 & 3 \\
3 & 2 & 1 & 6 \\
2 & 3 & 6 & 1
\end{array}\right)\)