Elliptic curves in class 71.4-c over 6.6.300125.1
Isogeny class 71.4-c contains
4 curves linked by isogenies of
degrees dividing 6.
| Curve label |
Weierstrass Coefficients |
| 71.4-c1
| \( \bigl[-a^{5} + 8 a^{3} + 4 a^{2} - 7 a - 1\) , \( -6 a^{5} + a^{4} + 44 a^{3} + 23 a^{2} - 29 a - 11\) , \( -a^{5} + 8 a^{3} + 4 a^{2} - 7 a\) , \( 24 a^{5} - 63 a^{4} - 44 a^{3} + 68 a^{2} + 5 a - 6\) , \( 297 a^{5} - 821 a^{4} - 439 a^{3} + 939 a^{2} - 86 a - 98\bigr] \)
|
| 71.4-c2
| \( \bigl[-8 a^{5} + 2 a^{4} + 58 a^{3} + 27 a^{2} - 38 a - 11\) , \( -a^{5} + 8 a^{3} + 5 a^{2} - 9 a - 4\) , \( -a^{5} + 8 a^{3} + 5 a^{2} - 7 a - 2\) , \( 24 a^{5} - 21 a^{4} - 145 a^{3} - 27 a^{2} + 88 a + 6\) , \( 11 a^{5} - 92 a^{4} + 101 a^{3} + 251 a^{2} - 84 a - 106\bigr] \)
|
| 71.4-c3
| \( \bigl[-8 a^{5} + 2 a^{4} + 58 a^{3} + 27 a^{2} - 38 a - 11\) , \( -a^{5} + 8 a^{3} + 5 a^{2} - 9 a - 4\) , \( -a^{5} + 8 a^{3} + 5 a^{2} - 7 a - 2\) , \( -16 a^{5} + 4 a^{4} + 115 a^{3} + 53 a^{2} - 72 a - 19\) , \( 5 a^{5} - a^{4} - 36 a^{3} - 20 a^{2} + 21 a + 8\bigr] \)
|
| 71.4-c4
| \( \bigl[-3 a^{5} + 23 a^{3} + 14 a^{2} - 16 a - 6\) , \( -3 a^{5} + 23 a^{3} + 14 a^{2} - 16 a - 5\) , \( a^{5} - 7 a^{3} - 5 a^{2} + 2 a + 3\) , \( -42 a^{5} - 18 a^{4} + 323 a^{3} + 285 a^{2} - 118 a - 210\) , \( 84 a^{5} - 417 a^{4} - 158 a^{3} + 1621 a^{2} + 169 a - 898\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrr}
1 & 6 & 2 & 3 \\
6 & 1 & 3 & 2 \\
2 & 3 & 1 & 6 \\
3 & 2 & 6 & 1
\end{array}\right)\)
