Elliptic curves in class 71.2-b over 6.6.434581.1
Isogeny class 71.2-b contains
4 curves linked by isogenies of
degrees dividing 6.
| Curve label |
Weierstrass Coefficients |
| 71.2-b1
| \( \bigl[2 a^{5} - 4 a^{4} - 7 a^{3} + 9 a^{2} + 3 a - 3\) , \( 2 a^{5} - 5 a^{4} - 5 a^{3} + 11 a^{2} - 4\) , \( a^{5} - 2 a^{4} - 4 a^{3} + 5 a^{2} + 4 a - 1\) , \( 10 a^{5} - 30 a^{4} - 16 a^{3} + 72 a^{2} - 2 a - 32\) , \( a^{5} + 3 a^{4} - 24 a^{3} + 25 a^{2} + 18 a - 26\bigr] \)
|
| 71.2-b2
| \( \bigl[a^{5} - 2 a^{4} - 4 a^{3} + 5 a^{2} + 4 a - 2\) , \( -2 a^{5} + 4 a^{4} + 7 a^{3} - 8 a^{2} - 5 a + 1\) , \( a^{5} - 2 a^{4} - 3 a^{3} + 4 a^{2} + a - 1\) , \( 3 a^{5} - 5 a^{4} - 12 a^{3} + 9 a^{2} + 7 a - 2\) , \( 6 a^{5} - 16 a^{4} - 17 a^{3} + 45 a^{2} + 9 a - 20\bigr] \)
|
| 71.2-b3
| \( \bigl[a^{5} - a^{4} - 5 a^{3} + 5 a + 1\) , \( -3 a^{5} + 6 a^{4} + 10 a^{3} - 12 a^{2} - 5 a + 3\) , \( a^{5} - 2 a^{4} - 3 a^{3} + 4 a^{2} - 1\) , \( -2 a^{5} + 3 a^{4} + 8 a^{3} - 4 a^{2} - 5 a + 2\) , \( -a^{5} + 2 a^{4} + 3 a^{3} - 4 a^{2} + 2\bigr] \)
|
| 71.2-b4
| \( \bigl[a^{5} - a^{4} - 5 a^{3} + 5 a + 1\) , \( -3 a^{5} + 6 a^{4} + 10 a^{3} - 12 a^{2} - 5 a + 3\) , \( a^{5} - 2 a^{4} - 3 a^{3} + 4 a^{2} - 1\) , \( -2 a^{5} + 3 a^{4} + 13 a^{3} - 9 a^{2} - 25 a - 8\) , \( 11 a^{5} - 17 a^{4} - 50 a^{3} + 24 a^{2} + 58 a + 16\bigr] \)
|
Rank: \( 1 \)
\(\left(\begin{array}{rrrr}
1 & 2 & 6 & 3 \\
2 & 1 & 3 & 6 \\
6 & 3 & 1 & 2 \\
3 & 6 & 2 & 1
\end{array}\right)\)
