Elliptic curves in class 43.3-c over 6.6.905177.1
Isogeny class 43.3-c contains
4 curves linked by isogenies of
degrees dividing 4.
| Curve label |
Weierstrass Coefficients |
| 43.3-c1
| \( \bigl[2 a^{5} + a^{4} - 13 a^{3} - a^{2} + 15 a + 2\) , \( a^{5} - a^{4} - 8 a^{3} + 6 a^{2} + 8 a - 1\) , \( 2 a^{5} + a^{4} - 12 a^{3} + 13 a + 1\) , \( -28 a^{5} - 17 a^{4} + 137 a^{3} - 31 a^{2} - 89 a - 8\) , \( 36 a^{5} + 166 a^{4} - 31 a^{3} - 502 a^{2} + 151 a + 21\bigr] \)
|
| 43.3-c2
| \( \bigl[2 a^{5} + a^{4} - 13 a^{3} - a^{2} + 15 a + 2\) , \( a^{5} - a^{4} - 8 a^{3} + 6 a^{2} + 8 a - 1\) , \( 2 a^{5} + a^{4} - 12 a^{3} + 13 a + 1\) , \( -18 a^{5} - 17 a^{4} + 92 a^{3} + 19 a^{2} - 84 a - 8\) , \( -59 a^{5} - 51 a^{4} + 314 a^{3} + 53 a^{2} - 295 a - 31\bigr] \)
|
| 43.3-c3
| \( \bigl[a^{4} + a^{3} - 4 a^{2} - a + 1\) , \( -a^{5} + 7 a^{3} - a^{2} - 9 a - 3\) , \( a^{5} + a^{4} - 6 a^{3} - 3 a^{2} + 8 a + 3\) , \( 3 a^{5} - 2 a^{4} - 21 a^{3} + 19 a^{2} + 22 a - 16\) , \( 7 a^{5} - 9 a^{4} - 47 a^{3} + 73 a^{2} + 40 a - 73\bigr] \)
|
| 43.3-c4
| \( \bigl[a^{5} + a^{4} - 6 a^{3} - 3 a^{2} + 8 a + 3\) , \( -a^{4} + 7 a^{2} - 2 a - 7\) , \( a^{5} + a^{4} - 6 a^{3} - 3 a^{2} + 8 a + 3\) , \( 13 a^{5} + 8 a^{4} - 80 a^{3} - 14 a^{2} + 83 a + 16\) , \( -23 a^{5} - 12 a^{4} + 144 a^{3} + 13 a^{2} - 150 a - 22\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrr}
1 & 2 & 4 & 4 \\
2 & 1 & 2 & 2 \\
4 & 2 & 1 & 4 \\
4 & 2 & 4 & 1
\end{array}\right)\)
