Elliptic curves in class 71.1-c over 6.6.300125.1
Isogeny class 71.1-c contains
4 curves linked by isogenies of
degrees dividing 6.
| Curve label |
Weierstrass Coefficients |
| 71.1-c1
| \( \bigl[a^{5} - 7 a^{3} - 5 a^{2} + 3 a + 3\) , \( 5 a^{5} - a^{4} - 36 a^{3} - 18 a^{2} + 22 a + 7\) , \( a^{5} - 7 a^{3} - 5 a^{2} + 3 a + 2\) , \( -528 a^{5} + 146 a^{4} + 3805 a^{3} + 1699 a^{2} - 2485 a - 750\) , \( -3732 a^{5} + 1043 a^{4} + 26879 a^{3} + 11901 a^{2} - 17570 a - 5200\bigr] \)
|
| 71.1-c2
| \( \bigl[-a^{5} + 8 a^{3} + 5 a^{2} - 8 a - 3\) , \( a^{5} - 7 a^{3} - 5 a^{2} + 3 a + 2\) , \( -a^{5} + 8 a^{3} + 5 a^{2} - 8 a - 3\) , \( -5 a^{5} + 2 a^{4} + 36 a^{3} + 13 a^{2} - 24 a - 7\) , \( -6 a^{5} + 2 a^{4} + 43 a^{3} + 18 a^{2} - 27 a - 8\bigr] \)
|
| 71.1-c3
| \( \bigl[-4 a^{5} + a^{4} + 29 a^{3} + 14 a^{2} - 20 a - 7\) , \( a^{5} - a^{4} - 6 a^{3} + 2 a\) , \( -4 a^{5} + a^{4} + 29 a^{3} + 13 a^{2} - 19 a - 5\) , \( 6 a^{5} - 19 a^{4} - 16 a^{3} + 68 a^{2} - 19 a - 13\) , \( -302 a^{5} + 643 a^{4} + 1380 a^{3} - 2136 a^{2} + 291 a + 268\bigr] \)
|
| 71.1-c4
| \( \bigl[a^{5} - 7 a^{3} - 5 a^{2} + 3 a + 3\) , \( 5 a^{5} - a^{4} - 36 a^{3} - 18 a^{2} + 22 a + 7\) , \( a^{5} - 7 a^{3} - 5 a^{2} + 3 a + 2\) , \( -243 a^{5} + 51 a^{4} + 1770 a^{3} + 874 a^{2} - 1225 a - 500\) , \( -2706 a^{5} + 885 a^{4} + 19377 a^{3} + 7454 a^{2} - 13313 a - 3305\bigr] \)
|
Rank not yet determined.
\(\left(\begin{array}{rrrr}
1 & 3 & 6 & 2 \\
3 & 1 & 2 & 6 \\
6 & 2 & 1 & 3 \\
2 & 6 & 3 & 1
\end{array}\right)\)
