Elliptic curves in class 8.1-b over 4.4.16448.1
Isogeny class 8.1-b contains
4 curves linked by isogenies of
degrees dividing 4.
Curve label |
Weierstrass Coefficients |
8.1-b1
| \( \bigl[a^{3} - 2 a^{2} - 5 a\) , \( -a^{3} + 3 a^{2} + 3 a - 1\) , \( a^{3} - 2 a^{2} - 5 a\) , \( 180 a^{3} - 260 a^{2} - 1229 a - 672\) , \( 2832 a^{3} - 4126 a^{2} - 19235 a - 10441\bigr] \)
|
8.1-b2
| \( \bigl[0\) , \( a^{3} - 3 a^{2} - 4 a + 2\) , \( a^{3} - 3 a^{2} - 3 a + 2\) , \( 4 a^{3} - 14 a^{2} - 6 a + 7\) , \( 6 a^{3} - 18 a^{2} - 5 a + 7\bigr] \)
|
8.1-b3
| \( \bigl[2 a^{3} - 5 a^{2} - 7 a + 2\) , \( 0\) , \( a^{3} - 3 a^{2} - 3 a + 2\) , \( -4 a^{3} + 14 a^{2} + 17 a - 28\) , \( 12 a^{3} - 26 a^{2} - 58 a + 6\bigr] \)
|
8.1-b4
| \( \bigl[a^{3} - 3 a^{2} - 2 a + 2\) , \( -2 a^{3} + 5 a^{2} + 9 a - 1\) , \( a^{3} - 2 a^{2} - 4 a\) , \( -2 a^{3} + 5 a^{2} + 6 a + 3\) , \( -a^{2} + a\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrr}
1 & 4 & 4 & 2 \\
4 & 1 & 4 & 2 \\
4 & 4 & 1 & 2 \\
2 & 2 & 2 & 1
\end{array}\right)\)