Elliptic curves in class 17.1-c over 5.5.38569.1
Isogeny class 17.1-c contains
6 curves linked by isogenies of
degrees dividing 8.
| Curve label |
Weierstrass Coefficients |
| 17.1-c1
| \( \bigl[2 a^{4} + a^{3} - 9 a^{2} - 3 a + 5\) , \( a^{3} - 3 a + 1\) , \( 0\) , \( 46 a^{4} - 88 a^{3} - 358 a^{2} - 19 a - 1\) , \( -1595 a^{4} - 2131 a^{3} + 3507 a^{2} + 2621 a - 912\bigr] \)
|
| 17.1-c2
| \( \bigl[2 a^{4} + a^{3} - 9 a^{2} - 3 a + 5\) , \( a^{3} - 3 a + 1\) , \( 0\) , \( a^{4} + 2 a^{3} - 3 a^{2} - 4 a + 4\) , \( 0\bigr] \)
|
| 17.1-c3
| \( \bigl[-a^{4} + 5 a^{2} + a - 2\) , \( -2 a^{4} - a^{3} + 9 a^{2} + 3 a - 5\) , \( a^{2} - 2\) , \( -11 a^{4} + 28 a^{3} + 5 a^{2} - 40 a + 10\) , \( -87 a^{4} + 174 a^{3} + 98 a^{2} - 209 a + 46\bigr] \)
|
| 17.1-c4
| \( \bigl[-a^{4} + 5 a^{2} + a - 3\) , \( -a^{4} + a^{3} + 4 a^{2} - 4 a\) , \( 0\) , \( 72 a^{4} + 36 a^{3} - 313 a^{2} - 173 a + 70\) , \( -339 a^{4} - 336 a^{3} + 1494 a^{2} + 1418 a - 496\bigr] \)
|
| 17.1-c5
| \( \bigl[a^{4} + a^{3} - 4 a^{2} - 4 a + 2\) , \( 3 a^{4} + a^{3} - 14 a^{2} - 5 a + 6\) , \( a^{4} + a^{3} - 4 a^{2} - 4 a + 2\) , \( -335 a^{4} - 75 a^{3} + 1619 a^{2} + 424 a - 1189\) , \( -4388 a^{4} - 1128 a^{3} + 21464 a^{2} + 5822 a - 15755\bigr] \)
|
| 17.1-c6
| \( \bigl[-a^{4} + 5 a^{2} + a - 3\) , \( -a^{4} + a^{3} + 4 a^{2} - 4 a\) , \( 0\) , \( -28 a^{4} + 51 a^{3} + 17 a^{2} - 333 a + 90\) , \( -855 a^{4} - 796 a^{3} + 3008 a^{2} + 2115 a - 791\bigr] \)
|
Rank: \( 1 \)
\(\left(\begin{array}{rrrrrr}
1 & 8 & 4 & 2 & 8 & 4 \\
8 & 1 & 2 & 4 & 4 & 8 \\
4 & 2 & 1 & 2 & 2 & 4 \\
2 & 4 & 2 & 1 & 4 & 2 \\
8 & 4 & 2 & 4 & 1 & 8 \\
4 & 8 & 4 & 2 & 8 & 1
\end{array}\right)\)
