Elliptic curves in class 17.2-a over 5.5.24217.1
Isogeny class 17.2-a contains
4 curves linked by isogenies of
degrees dividing 4.
| Curve label |
Weierstrass Coefficients |
| 17.2-a1
| \( \bigl[a^{4} - 5 a^{2} + 3\) , \( -2 a^{4} + 2 a^{3} + 9 a^{2} - 7 a - 3\) , \( 3 a^{4} - a^{3} - 14 a^{2} + 3 a + 6\) , \( 68 a^{4} - 49 a^{3} - 301 a^{2} + 152 a + 71\) , \( -190 a^{4} + 134 a^{3} + 860 a^{2} - 410 a - 310\bigr] \)
|
| 17.2-a2
| \( \bigl[a^{4} - 5 a^{2} + 2\) , \( a\) , \( 0\) , \( -260 a^{4} + 96 a^{3} + 1264 a^{2} - 208 a - 704\) , \( -20 a^{4} + 7 a^{3} + 96 a^{2} - 17 a - 54\bigr] \)
|
| 17.2-a3
| \( \bigl[a^{4} - 5 a^{2} + 2\) , \( a\) , \( 0\) , \( 65 a^{4} - 24 a^{3} - 316 a^{2} + 52 a + 176\) , \( 0\bigr] \)
|
| 17.2-a4
| \( \bigl[a^{2} + a - 1\) , \( a\) , \( 0\) , \( -58 a^{4} + 26 a^{3} + 249 a^{2} - 55 a - 147\) , \( 201 a^{4} - 197 a^{3} - 1014 a^{2} + 219 a + 561\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrr}
1 & 2 & 4 & 4 \\
2 & 1 & 2 & 2 \\
4 & 2 & 1 & 4 \\
4 & 2 & 4 & 1
\end{array}\right)\)
