Elliptic curves in class 17.1-a over 5.5.24217.1
Isogeny class 17.1-a contains
4 curves linked by isogenies of
degrees dividing 4.
| Curve label |
Weierstrass Coefficients |
| 17.1-a1
| \( \bigl[a^{4} - 5 a^{2} + 3\) , \( -2 a^{4} + 2 a^{3} + 9 a^{2} - 7 a - 3\) , \( 1\) , \( 21 a^{4} + 14 a^{3} - 92 a^{2} - 79 a - 22\) , \( 74 a^{4} + 7 a^{3} - 324 a^{2} - 87 a + 12\bigr] \)
|
| 17.1-a2
| \( \bigl[a^{4} - a^{3} - 4 a^{2} + 4 a + 2\) , \( 3 a^{4} - 2 a^{3} - 14 a^{2} + 6 a + 7\) , \( -a^{4} + a^{3} + 5 a^{2} - 3 a - 3\) , \( -28 a^{4} + 14 a^{3} + 124 a^{2} - 21 a - 65\) , \( -92 a^{4} + 50 a^{3} + 410 a^{2} - 78 a - 227\bigr] \)
|
| 17.1-a3
| \( \bigl[2 a^{4} - a^{3} - 9 a^{2} + 3 a + 4\) , \( a^{4} - a^{3} - 5 a^{2} + 4 a + 4\) , \( 2 a^{4} - 9 a^{2} + 2\) , \( 5 a^{4} - 4 a^{3} - 23 a^{2} + 12 a + 9\) , \( 5 a^{4} - 2 a^{3} - 23 a^{2} + 4 a + 5\bigr] \)
|
| 17.1-a4
| \( \bigl[3 a^{4} - a^{3} - 14 a^{2} + 3 a + 5\) , \( -a^{2} - a + 1\) , \( 0\) , \( -115 a^{4} + 41 a^{3} + 555 a^{2} - 83 a - 318\) , \( -757 a^{4} + 282 a^{3} + 3694 a^{2} - 572 a - 2090\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrr}
1 & 2 & 4 & 4 \\
2 & 1 & 2 & 2 \\
4 & 2 & 1 & 4 \\
4 & 2 & 4 & 1
\end{array}\right)\)
