Elliptic curves in class 7.1-a over 4.4.19429.1
Isogeny class 7.1-a contains
4 curves linked by isogenies of
degrees dividing 6.
Curve label |
Weierstrass Coefficients |
7.1-a1
| \( \bigl[a^{2} - a - 3\) , \( a^{3} - 2 a^{2} - 3 a + 3\) , \( 0\) , \( 4 a^{3} + 2 a^{2} - 46 a - 63\) , \( -42 a^{3} - 3 a^{2} + 207 a + 150\bigr] \)
|
7.1-a2
| \( \bigl[a^{2} - a - 3\) , \( a^{3} - 2 a^{2} - 3 a + 3\) , \( 0\) , \( -a^{3} - 3 a^{2} - a + 2\) , \( -12 a^{3} - 22 a^{2} + 9 a + 21\bigr] \)
|
7.1-a3
| \( \bigl[a^{3} - 2 a^{2} - 4 a + 3\) , \( a^{3} - 3 a^{2} - 3 a + 6\) , \( a^{3} - 2 a^{2} - 4 a + 3\) , \( 2 a^{3} + 2 a^{2} - 2 a + 1\) , \( a^{3} - 28 a^{2} - 10 a + 24\bigr] \)
|
7.1-a4
| \( \bigl[a^{3} - 2 a^{2} - 4 a + 3\) , \( a^{3} - 3 a^{2} - 3 a + 6\) , \( a^{3} - 2 a^{2} - 4 a + 3\) , \( 2 a^{3} - 8 a^{2} - 7 a + 11\) , \( a^{3} - 5 a^{2} - 4 a + 6\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrr}
1 & 2 & 3 & 6 \\
2 & 1 & 6 & 3 \\
3 & 6 & 1 & 2 \\
6 & 3 & 2 & 1
\end{array}\right)\)