Elliptic curves in class 7.2-a over 4.4.4205.1
Isogeny class 7.2-a contains
4 curves linked by isogenies of
degrees dividing 10.
| Curve label |
Weierstrass Coefficients |
| 7.2-a1
| \( \bigl[a^{2} - a - 2\) , \( -a^{3} + 2 a^{2} + 4 a\) , \( -a^{3} + 2 a^{2} + 4 a\) , \( -17 a^{3} + 28 a^{2} + 65 a - 28\) , \( -39 a^{3} + 66 a^{2} + 150 a - 70\bigr] \)
|
| 7.2-a2
| \( \bigl[a^{2} - a - 2\) , \( -a^{3} + 2 a^{2} + 4 a\) , \( -a^{3} + 2 a^{2} + 4 a\) , \( -2 a^{3} + 3 a^{2} + 10 a + 2\) , \( -a^{3} + 2 a^{2} + 5 a - 1\bigr] \)
|
| 7.2-a3
| \( \bigl[a^{3} - a^{2} - 5 a\) , \( -a^{2} + 3 a + 3\) , \( a^{3} - a^{2} - 5 a - 1\) , \( -17 a^{3} + 28 a^{2} + 64 a - 29\) , \( 39 a^{3} - 63 a^{2} - 164 a + 42\bigr] \)
|
| 7.2-a4
| \( \bigl[a^{3} - a^{2} - 5 a\) , \( -a^{2} + 3 a + 3\) , \( a^{3} - a^{2} - 5 a - 1\) , \( -2 a^{3} + 3 a^{2} + 9 a + 1\) , \( 1\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrr}
1 & 2 & 5 & 10 \\
2 & 1 & 10 & 5 \\
5 & 10 & 1 & 2 \\
10 & 5 & 2 & 1
\end{array}\right)\)
