Elliptic curves in class 17.1-a over 4.4.9792.1
Isogeny class 17.1-a contains
4 curves linked by isogenies of
degrees dividing 6.
Curve label |
Weierstrass Coefficients |
17.1-a1
| \( \bigl[-a^{3} + 4 a^{2} + 2 a - 7\) , \( a^{3} - 3 a^{2} - 3 a + 3\) , \( 1\) , \( -62 a^{3} + 192 a^{2} + 210 a - 313\) , \( 255 a^{3} - 872 a^{2} - 674 a + 1751\bigr] \)
|
17.1-a2
| \( \bigl[a^{2} - a - 3\) , \( -a^{2} + 2 a + 3\) , \( a^{3} - 3 a^{2} - 3 a + 5\) , \( a^{3} - 4 a^{2} + 3 a + 12\) , \( 3 a^{3} - 9 a^{2} - a + 16\bigr] \)
|
17.1-a3
| \( \bigl[-a^{3} + 4 a^{2} + 2 a - 7\) , \( 2 a^{3} - 7 a^{2} - 3 a + 12\) , \( 1\) , \( -226 a^{3} + 751 a^{2} + 653 a - 1418\) , \( 2180 a^{3} - 7069 a^{2} - 6601 a + 12877\bigr] \)
|
17.1-a4
| \( \bigl[-a^{3} + 4 a^{2} + 2 a - 7\) , \( 2 a^{3} - 7 a^{2} - 3 a + 12\) , \( 1\) , \( -a^{3} + 11 a^{2} - 7 a - 33\) , \( 10 a^{3} - 10 a^{2} - 68 a - 49\bigr] \)
|
Rank: \( 1 \)
\(\left(\begin{array}{rrrr}
1 & 3 & 2 & 6 \\
3 & 1 & 6 & 2 \\
2 & 6 & 1 & 3 \\
6 & 2 & 3 & 1
\end{array}\right)\)