Elliptic curves in class 17.2-c over 4.4.8069.1
Isogeny class 17.2-c contains
4 curves linked by isogenies of
degrees dividing 6.
| Curve label |
Weierstrass Coefficients |
| 17.2-c1
| \( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( 0\) , \( a^{3} + a^{2} - 3 a - 2\) , \( -4 a^{3} - 4 a^{2} + 12 a - 7\) , \( -27 a^{3} - 32 a^{2} + 65 a + 19\bigr] \)
|
| 17.2-c2
| \( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( 0\) , \( a^{3} + a^{2} - 3 a - 2\) , \( a^{3} + a^{2} - 3 a - 2\) , \( a^{3} + a^{2} - 3 a - 1\bigr] \)
|
| 17.2-c3
| \( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( 0\) , \( a^{3} + a^{2} - 3 a - 2\) , \( -24 a^{3} - 29 a^{2} + 57 a + 13\) , \( -236 a^{3} - 271 a^{2} + 600 a + 109\bigr] \)
|
| 17.2-c4
| \( \bigl[1\) , \( -a^{2} - a + 4\) , \( a^{3} + a^{2} - 4 a - 1\) , \( 121 a^{3} + 56 a^{2} - 553 a - 264\) , \( 97 a^{2} + 46 a - 550\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrr}
1 & 2 & 6 & 3 \\
2 & 1 & 3 & 6 \\
6 & 3 & 1 & 2 \\
3 & 6 & 2 & 1
\end{array}\right)\)
