Elliptic curves in class 12.2-e over 4.4.13768.1
Isogeny class 12.2-e contains
6 curves linked by isogenies of
degrees dividing 8.
| Curve label |
Weierstrass Coefficients |
| 12.2-e1
| \( \bigl[a^{2} - 3\) , \( a^{2} - 3\) , \( a^{2} - 2\) , \( 5 a - 8\) , \( 4 a^{3} - 8 a^{2} - 8 a + 9\bigr] \)
|
| 12.2-e2
| \( \bigl[a^{2} - 3\) , \( -a^{3} + 5 a + 2\) , \( a^{3} - 4 a - 1\) , \( -a^{3} + a^{2} + a - 1\) , \( -a^{3} + 5 a - 3\bigr] \)
|
| 12.2-e3
| \( \bigl[a^{3} - a^{2} - 3 a + 1\) , \( a - 1\) , \( a^{3} - a^{2} - 4 a + 2\) , \( -23 a^{3} + 36 a^{2} + 94 a - 114\) , \( -117 a^{3} + 178 a^{2} + 515 a - 461\bigr] \)
|
| 12.2-e4
| \( \bigl[a^{3} - a^{2} - 3 a + 1\) , \( a - 1\) , \( a^{3} - a^{2} - 4 a + 2\) , \( -3 a^{3} + a^{2} + 9 a - 9\) , \( -a^{3} + 5 a^{2} + 8 a - 10\bigr] \)
|
| 12.2-e5
| \( \bigl[a + 1\) , \( -a^{3} + a^{2} + 3 a\) , \( a^{3} - a^{2} - 3 a + 1\) , \( 14 a^{3} - 11 a^{2} - 53 a - 29\) , \( -a^{3} - 54 a^{2} + 116 a + 67\bigr] \)
|
| 12.2-e6
| \( \bigl[a + 1\) , \( -a^{3} + a^{2} + 3 a\) , \( a^{3} - a^{2} - 3 a + 1\) , \( -21 a^{3} - 11 a^{2} + 127 a + 86\) , \( -225 a^{3} - 22 a^{2} + 1280 a + 567\bigr] \)
|
Rank: \( 1 \)
\(\left(\begin{array}{rrrrrr}
1 & 8 & 8 & 4 & 2 & 4 \\
8 & 1 & 4 & 2 & 4 & 8 \\
8 & 4 & 1 & 2 & 4 & 8 \\
4 & 2 & 2 & 1 & 2 & 4 \\
2 & 4 & 4 & 2 & 1 & 2 \\
4 & 8 & 8 & 4 & 2 & 1
\end{array}\right)\)
