Elliptic curves in class 8.1-c over 4.4.11324.1
Isogeny class 8.1-c contains
4 curves linked by isogenies of
degrees dividing 4.
| Curve label |
Weierstrass Coefficients |
| 8.1-c1
| \( \bigl[a^{3} + a^{2} - 4 a - 3\) , \( -a^{3} - a^{2} + 3 a + 3\) , \( a\) , \( -7 a^{3} + 32 a + 4\) , \( -5 a^{3} - 2 a^{2} + 24 a + 12\bigr] \)
|
| 8.1-c2
| \( \bigl[a^{3} + a^{2} - 3 a - 3\) , \( a^{2} + a - 3\) , \( a^{3} - 4 a\) , \( 242 a^{3} - 718 a^{2} + 323 a + 220\) , \( 6877 a^{3} - 21198 a^{2} + 9972 a + 6560\bigr] \)
|
| 8.1-c3
| \( \bigl[a^{3} - 3 a + 1\) , \( -a^{3} + a^{2} + 3 a - 2\) , \( a^{3} - 4 a + 1\) , \( -a^{3} + a^{2} - 1\) , \( -3 a^{3} - 2 a^{2} + 5 a\bigr] \)
|
| 8.1-c4
| \( \bigl[1\) , \( 0\) , \( a^{3} + a^{2} - 3 a - 3\) , \( -3 a^{3} + 4 a^{2} + 12 a - 19\) , \( -2 a^{2} - 2 a + 4\bigr] \)
|
Rank: \( 1 \)
\(\left(\begin{array}{rrrr}
1 & 4 & 4 & 2 \\
4 & 1 & 4 & 2 \\
4 & 4 & 1 & 2 \\
2 & 2 & 2 & 1
\end{array}\right)\)
