Elliptic curves in class 9.1-b over 4.4.8112.1
Isogeny class 9.1-b contains
4 curves linked by isogenies of
degrees dividing 6.
Curve label |
Weierstrass Coefficients |
9.1-b1
| \( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( a^{3} + a^{2} - 3 a - 4\) , \( a^{3} - 4 a\) , \( 2 a^{3} + 4 a^{2} - 4 a - 6\) , \( -a^{3} + 6 a + 3\bigr] \)
|
9.1-b2
| \( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( -a^{3} + a^{2} + 3 a - 4\) , \( 1\) , \( a^{3} - a^{2} - 3 a + 4\) , \( 2 a^{3} - 2 a^{2} - 6 a + 5\bigr] \)
|
9.1-b3
| \( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( -1\) , \( a^{3} + a^{2} - 3 a - 3\) , \( 27 a^{3} + 22 a^{2} - 116 a - 96\) , \( 127 a^{3} + 106 a^{2} - 546 a - 456\bigr] \)
|
9.1-b4
| \( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( -1\) , \( a^{2} + a - 2\) , \( -26 a^{3} + 21 a^{2} + 111 a - 92\) , \( -105 a^{3} + 87 a^{2} + 451 a - 376\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrr}
1 & 2 & 6 & 3 \\
2 & 1 & 3 & 6 \\
6 & 3 & 1 & 2 \\
3 & 6 & 2 & 1
\end{array}\right)\)