Elliptic curves in class 12.1-f over 4.4.15952.1
Isogeny class 12.1-f contains
4 curves linked by isogenies of
degrees dividing 4.
| Curve label |
Weierstrass Coefficients |
| 12.1-f1
| \( \bigl[a^{3} - 6 a - 1\) , \( -a^{2} + a + 4\) , \( a^{2} - 3\) , \( -3 a^{3} - 2 a^{2} + 11 a + 1\) , \( -13 a^{3} - 2 a^{2} + 51 a - 19\bigr] \)
|
| 12.1-f2
| \( \bigl[a^{3} - 6 a - 1\) , \( -a^{2} + a + 4\) , \( a^{3} - 5 a\) , \( -20 a^{3} - 46 a^{2} + 2 a + 15\) , \( -173 a^{3} - 439 a^{2} - 91 a + 74\bigr] \)
|
| 12.1-f3
| \( \bigl[a^{3} - 5 a\) , \( -a^{3} + a^{2} + 5 a - 2\) , \( a^{3} - 5 a\) , \( 8 a^{3} - 22 a^{2} + 4 a - 2\) , \( 69 a^{3} - 156 a^{2} - 67 a + 29\bigr] \)
|
| 12.1-f4
| \( \bigl[0\) , \( -a^{2} + 2\) , \( a^{2} - a - 2\) , \( 2 a^{3} - 2 a^{2} - 5 a - 1\) , \( 3 a^{3} - 7 a^{2} - 4 a + 1\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrr}
1 & 4 & 2 & 4 \\
4 & 1 & 2 & 4 \\
2 & 2 & 1 & 2 \\
4 & 4 & 2 & 1
\end{array}\right)\)
