Elliptic curves in class 7.1-a over 4.4.1957.1
Isogeny class 7.1-a contains
4 curves linked by isogenies of
degrees dividing 6.
Curve label |
Weierstrass Coefficients |
7.1-a1
| \( \bigl[a^{2} - a - 1\) , \( -a^{3} + a^{2} + 3 a - 2\) , \( a^{2} - a - 1\) , \( 32 a^{3} - 57 a^{2} - 33 a + 17\) , \( 204 a^{3} - 364 a^{2} - 182 a + 118\bigr] \)
|
7.1-a2
| \( \bigl[-a^{3} + a^{2} + 3 a\) , \( a^{3} - 5 a\) , \( -a^{3} + a^{2} + 3 a - 1\) , \( a^{2} - 3 a\) , \( -a^{3} + a^{2} + a\bigr] \)
|
7.1-a3
| \( \bigl[-a^{3} + a^{2} + 3 a\) , \( a^{3} - 5 a\) , \( -a^{3} + a^{2} + 3 a - 1\) , \( -5 a^{3} - 4 a^{2} + 7 a + 5\) , \( -6 a^{3} - 8 a^{2} - 3\bigr] \)
|
7.1-a4
| \( \bigl[a + 1\) , \( -a^{2} + a + 1\) , \( a^{3} - 3 a\) , \( -a^{3} - 4 a^{2} - 6 a + 1\) , \( -5 a^{3} - 11 a^{2} - a + 3\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrr}
1 & 6 & 3 & 2 \\
6 & 1 & 2 & 3 \\
3 & 2 & 1 & 6 \\
2 & 3 & 6 & 1
\end{array}\right)\)