Elliptic curves in class 71.4-a over 6.6.434581.1
Isogeny class 71.4-a contains
4 curves linked by isogenies of
degrees dividing 6.
| Curve label |
Weierstrass Coefficients |
| 71.4-a1
| \( \bigl[a^{5} - 2 a^{4} - 4 a^{3} + 5 a^{2} + 4 a - 2\) , \( a^{5} - 4 a^{4} + 10 a^{2} - 2 a - 4\) , \( 2 a^{5} - 5 a^{4} - 5 a^{3} + 11 a^{2} + a - 2\) , \( 10 a^{5} - 16 a^{4} - 43 a^{3} + 30 a^{2} + 35 a + 2\) , \( -8 a^{5} + 11 a^{4} + 39 a^{3} - 17 a^{2} - 45 a - 16\bigr] \)
|
| 71.4-a2
| \( \bigl[a\) , \( -a^{5} + 2 a^{4} + 4 a^{3} - 4 a^{2} - 4 a + 2\) , \( 2 a^{5} - 5 a^{4} - 5 a^{3} + 11 a^{2} + 2 a - 2\) , \( -22 a^{5} + 59 a^{4} + 46 a^{3} - 134 a^{2} + 11 a + 22\) , \( 58 a^{5} - 154 a^{4} - 124 a^{3} + 357 a^{2} - 24 a - 72\bigr] \)
|
| 71.4-a3
| \( \bigl[a\) , \( -a^{5} + 2 a^{4} + 4 a^{3} - 4 a^{2} - 4 a + 2\) , \( 2 a^{5} - 5 a^{4} - 5 a^{3} + 11 a^{2} + 2 a - 2\) , \( -42 a^{5} + 69 a^{4} + 171 a^{3} - 109 a^{2} - 144 a - 53\) , \( 229 a^{5} - 414 a^{4} - 913 a^{3} + 730 a^{2} + 753 a + 161\bigr] \)
|
| 71.4-a4
| \( \bigl[a^{5} - 2 a^{4} - 4 a^{3} + 5 a^{2} + 4 a - 2\) , \( a^{5} - 4 a^{4} + 10 a^{2} - 2 a - 4\) , \( 2 a^{5} - 5 a^{4} - 5 a^{3} + 11 a^{2} + a - 2\) , \( -20 a^{5} + 24 a^{4} + 107 a^{3} - 35 a^{2} - 140 a - 48\) , \( -79 a^{5} + 98 a^{4} + 368 a^{3} - 88 a^{2} - 342 a - 103\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrr}
1 & 3 & 6 & 2 \\
3 & 1 & 2 & 6 \\
6 & 2 & 1 & 3 \\
2 & 6 & 3 & 1
\end{array}\right)\)
