Elliptic curves in class 4.1-c over 4.4.13824.1
Isogeny class 4.1-c contains
4 curves linked by isogenies of
degrees dividing 6.
| Curve label |
Weierstrass Coefficients |
| 4.1-c1
| \( \bigl[a^{2} - 2\) , \( -a^{3} + 3 a - 1\) , \( a^{3} - 3 a\) , \( 5 a^{3} - 14 a^{2} - 8 a + 19\) , \( -14 a^{3} + 29 a^{2} + 18 a - 38\bigr] \)
|
| 4.1-c2
| \( \bigl[a^{2} - 2\) , \( -a^{3} - a^{2} + 3 a + 2\) , \( a\) , \( -6 a^{3} - 14 a^{2} + 9 a + 19\) , \( -14 a^{3} - 30 a^{2} + 18 a + 38\bigr] \)
|
| 4.1-c3
| \( \bigl[a^{3} - 4 a\) , \( -a^{3} + a^{2} + 3 a - 3\) , \( a^{3} + a^{2} - 4 a - 2\) , \( a^{3} + 5 a^{2} - 8 a - 19\) , \( -2 a^{3} - a^{2} + 7 a + 5\bigr] \)
|
| 4.1-c4
| \( \bigl[a^{3} - 4 a\) , \( -a^{3} + 3 a\) , \( a^{2} - 2\) , \( -3 a^{3} + 3 a^{2} + 12 a - 10\) , \( -4 a^{3} + 4 a^{2} + 18 a - 19\bigr] \)
|
Rank: \( 1 \)
\(\left(\begin{array}{rrrr}
1 & 3 & 2 & 6 \\
3 & 1 & 6 & 2 \\
2 & 6 & 1 & 3 \\
6 & 2 & 3 & 1
\end{array}\right)\)
