Elliptic curves in class 12.1-f over 4.4.13068.1
Isogeny class 12.1-f contains
6 curves linked by isogenies of
degrees dividing 8.
| Curve label |
Weierstrass Coefficients |
| 12.1-f1
| \( \bigl[-a^{3} + 2 a^{2} + 4 a - 2\) , \( -1\) , \( a^{2} - a - 3\) , \( -4 a^{3} + 4 a^{2} + 28 a + 11\) , \( 19 a^{3} - 19 a^{2} - 133 a - 65\bigr] \)
|
| 12.1-f2
| \( \bigl[-a^{3} + 2 a^{2} + 4 a - 2\) , \( -a^{3} + a^{2} + 7 a + 1\) , \( 0\) , \( -6 a^{3} + 6 a^{2} + 42 a - 19\) , \( 15 a^{3} - 15 a^{2} - 105 a + 37\bigr] \)
|
| 12.1-f3
| \( \bigl[-a^{3} + 2 a^{2} + 4 a - 2\) , \( -a^{3} + a^{2} + 7 a + 1\) , \( 0\) , \( -a^{3} + a^{2} + 7 a + 1\) , \( 1\bigr] \)
|
| 12.1-f4
| \( \bigl[a^{3} - a^{2} - 6 a - 1\) , \( -2 a^{3} + 3 a^{2} + 9 a\) , \( -a^{3} + 2 a^{2} + 5 a - 2\) , \( -11 a^{3} + 29 a^{2} + 13 a + 3\) , \( -872 a^{3} + 2458 a^{2} + 752 a - 475\bigr] \)
|
| 12.1-f5
| \( \bigl[a\) , \( -a^{3} + 2 a^{2} + 5 a - 2\) , \( a^{2} - a - 2\) , \( -2 a^{3} + 2 a^{2} + 6 a - 3\) , \( -a^{3} - 6 a^{2} - 6 a + 1\bigr] \)
|
| 12.1-f6
| \( \bigl[a\) , \( -a^{3} + 2 a^{2} + 5 a - 2\) , \( a^{2} - a - 2\) , \( 3 a^{3} - 33 a^{2} - 69 a + 7\) , \( -107 a^{3} - 151 a^{2} + 63 a - 34\bigr] \)
|
Rank: \( 1 \)
\(\left(\begin{array}{rrrrrr}
1 & 8 & 4 & 8 & 2 & 4 \\
8 & 1 & 2 & 4 & 4 & 8 \\
4 & 2 & 1 & 2 & 2 & 4 \\
8 & 4 & 2 & 1 & 4 & 8 \\
2 & 4 & 2 & 4 & 1 & 2 \\
4 & 8 & 4 & 8 & 2 & 1
\end{array}\right)\)
