Elliptic curves in class 17.1-b over 6.6.1541581.1
Isogeny class 17.1-b contains
4 curves linked by isogenies of
degrees dividing 6.
| Curve label |
Weierstrass Coefficients |
| 17.1-b1
| \( \bigl[a^{5} - 2 a^{4} - 4 a^{3} + 5 a^{2} + 4 a\) , \( a^{5} - 3 a^{4} - 2 a^{3} + 8 a^{2} - 2\) , \( 2 a^{5} - 3 a^{4} - 9 a^{3} + 6 a^{2} + 10 a + 1\) , \( -30 a^{5} + 12 a^{4} + 207 a^{3} + 20 a^{2} - 315 a - 131\) , \( 202 a^{5} - 140 a^{4} - 1264 a^{3} + 38 a^{2} + 1851 a + 728\bigr] \)
|
| 17.1-b2
| \( \bigl[2 a^{5} - 4 a^{4} - 7 a^{3} + 10 a^{2} + 5 a - 2\) , \( -a^{5} + 2 a^{4} + 3 a^{3} - 4 a^{2} - 2 a + 1\) , \( 2 a^{5} - 4 a^{4} - 8 a^{3} + 11 a^{2} + 9 a - 2\) , \( -19 a^{5} + 16 a^{4} + 112 a^{3} - 10 a^{2} - 159 a - 63\) , \( -35 a^{5} + 29 a^{4} + 207 a^{3} - 22 a^{2} - 295 a - 115\bigr] \)
|
| 17.1-b3
| \( \bigl[2 a^{5} - 3 a^{4} - 9 a^{3} + 6 a^{2} + 9 a + 1\) , \( -3 a^{5} + 7 a^{4} + 9 a^{3} - 18 a^{2} - 4 a + 4\) , \( a^{5} - a^{4} - 6 a^{3} + 3 a^{2} + 8 a - 1\) , \( -17 a^{5} + 23 a^{4} + 93 a^{3} - 64 a^{2} - 125 a + 20\) , \( 50 a^{5} - 82 a^{4} - 254 a^{3} + 274 a^{2} + 313 a - 189\bigr] \)
|
| 17.1-b4
| \( \bigl[a^{5} - a^{4} - 6 a^{3} + 3 a^{2} + 9 a\) , \( -a^{5} + 3 a^{4} + 3 a^{3} - 10 a^{2} - 4 a + 4\) , \( a^{5} - 2 a^{4} - 4 a^{3} + 6 a^{2} + 4 a - 1\) , \( -2 a^{5} + 3 a^{4} + 9 a^{3} - 9 a^{2} - 8 a + 7\) , \( -a^{5} + 3 a^{4} + 4 a^{3} - 10 a^{2} - 5 a + 4\bigr] \)
|
Rank: \( 1 \)
\(\left(\begin{array}{rrrr}
1 & 2 & 3 & 6 \\
2 & 1 & 6 & 3 \\
3 & 6 & 1 & 2 \\
6 & 3 & 2 & 1
\end{array}\right)\)
