Elliptic curves in class 71.4-b over 6.6.434581.1
Isogeny class 71.4-b contains
4 curves linked by isogenies of
degrees dividing 6.
| Curve label |
Weierstrass Coefficients |
| 71.4-b1
| \( \bigl[3 a^{5} - 6 a^{4} - 10 a^{3} + 12 a^{2} + 5 a - 2\) , \( -a^{5} + 3 a^{4} + 2 a^{3} - 9 a^{2} + 2 a + 3\) , \( a^{5} - a^{4} - 5 a^{3} + 5 a + 2\) , \( -7 a^{5} + 39 a^{3} + 33 a^{2} - 19 a - 18\) , \( 265 a^{5} - 188 a^{4} - 1291 a^{3} - 356 a^{2} + 551 a + 188\bigr] \)
|
| 71.4-b2
| \( \bigl[a\) , \( a^{5} - 2 a^{4} - 3 a^{3} + 3 a^{2} + 2 a\) , \( a^{5} - a^{4} - 5 a^{3} + a^{2} + 4 a\) , \( -3 a^{5} + 8 a^{4} + 5 a^{3} - 17 a^{2} + 4 a + 3\) , \( 3 a^{5} - 8 a^{4} - 7 a^{3} + 17 a^{2} - a - 3\bigr] \)
|
| 71.4-b3
| \( \bigl[2 a^{5} - 5 a^{4} - 5 a^{3} + 11 a^{2} + 2 a - 2\) , \( 3 a^{5} - 7 a^{4} - 8 a^{3} + 15 a^{2} + 2 a - 3\) , \( 2 a^{5} - 5 a^{4} - 5 a^{3} + 12 a^{2} - 4\) , \( 4 a^{5} - 10 a^{4} - 10 a^{3} + 23 a^{2} + 2 a - 4\) , \( 2 a^{5} - 5 a^{4} - 5 a^{3} + 12 a^{2} - 3\bigr] \)
|
| 71.4-b4
| \( \bigl[2 a^{5} - 5 a^{4} - 5 a^{3} + 11 a^{2} + 2 a - 2\) , \( 3 a^{5} - 7 a^{4} - 8 a^{3} + 15 a^{2} + 2 a - 3\) , \( 2 a^{5} - 5 a^{4} - 5 a^{3} + 12 a^{2} - 4\) , \( -6 a^{5} + 15 a^{4} + 15 a^{3} - 37 a^{2} + 7 a + 1\) , \( a^{5} - 5 a^{4} - 2 a^{3} + 30 a^{2} - 16 a - 16\bigr] \)
|
Rank: \( 1 \)
\(\left(\begin{array}{rrrr}
1 & 2 & 6 & 3 \\
2 & 1 & 3 & 6 \\
6 & 3 & 1 & 2 \\
3 & 6 & 2 & 1
\end{array}\right)\)
