Elliptic curves in class 17.2-c over 4.4.7168.1
Isogeny class 17.2-c contains
4 curves linked by isogenies of
degrees dividing 6.
| Curve label |
Weierstrass Coefficients |
| 17.2-c1
| \( \bigl[a^{2} + a - 2\) , \( a^{3} - 3 a\) , \( a^{2} + a - 3\) , \( 2 a^{3} - a^{2} - 2 a + 1\) , \( -4 a^{3} + 12 a^{2} + 7 a - 20\bigr] \)
|
| 17.2-c2
| \( \bigl[a^{2} - 3\) , \( -a^{3} + 4 a\) , \( a\) , \( -a\) , \( -1\bigr] \)
|
| 17.2-c3
| \( \bigl[a^{2} - 3\) , \( -a^{3} + 4 a\) , \( a\) , \( 65 a^{3} + 80 a^{2} - 296 a - 370\) , \( -513 a^{3} - 652 a^{2} + 2247 a + 2840\bigr] \)
|
| 17.2-c4
| \( \bigl[a^{2} + a - 2\) , \( a^{3} - 3 a\) , \( a^{2} + a - 3\) , \( -8 a^{3} - a^{2} + 73 a - 74\) , \( 131 a^{3} - 218 a^{2} - 442 a + 641\bigr] \)
|
Rank: \( 1 \)
\(\left(\begin{array}{rrrr}
1 & 2 & 6 & 3 \\
2 & 1 & 3 & 6 \\
6 & 3 & 1 & 2 \\
3 & 6 & 2 & 1
\end{array}\right)\)
