Elliptic curves in class 17.1-a over 4.4.2624.1
Isogeny class 17.1-a contains
4 curves linked by isogenies of
degrees dividing 6.
Curve label |
Weierstrass Coefficients |
17.1-a1
| \( \bigl[1\) , \( a^{2} - a\) , \( a^{2} - 2 a\) , \( 9 a^{3} - 5 a^{2} + a\) , \( 25 a^{3} - 27 a^{2} - 2 a + 3\bigr] \)
|
17.1-a2
| \( \bigl[a^{3} - 2 a^{2} - a + 2\) , \( a^{3} - 3 a^{2} + 1\) , \( 1\) , \( -2 a^{3} + 17 a^{2} - 14 a - 50\) , \( -110 a^{3} + 288 a^{2} + 190 a - 406\bigr] \)
|
17.1-a3
| \( \bigl[a^{3} - 2 a^{2} - a + 2\) , \( a^{3} - 3 a^{2} + 1\) , \( 1\) , \( -2 a^{3} + 7 a^{2} + a - 5\) , \( a^{3} - 2 a^{2} + 1\bigr] \)
|
17.1-a4
| \( \bigl[a^{3} - 2 a^{2} - a + 2\) , \( a^{3} - 3 a^{2} + 1\) , \( 1\) , \( 3 a^{3} - 3 a^{2} - 14 a\) , \( 2 a^{3} - 9 a^{2} + 3 a + 19\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrr}
1 & 2 & 3 & 6 \\
2 & 1 & 6 & 3 \\
3 & 6 & 1 & 2 \\
6 & 3 & 2 & 1
\end{array}\right)\)