Elliptic curves in class 12.2-d over 4.4.13768.1
Isogeny class 12.2-d contains
4 curves linked by isogenies of
degrees dividing 6.
| Curve label |
Weierstrass Coefficients |
| 12.2-d1
| \( \bigl[a^{3} - 5 a - 2\) , \( -a^{3} + 5 a + 1\) , \( a^{2} - 3\) , \( 20 a^{3} - 39 a^{2} - 79 a + 123\) , \( -33 a^{3} + 38 a^{2} + 146 a - 79\bigr] \)
|
| 12.2-d2
| \( \bigl[a^{2} - a - 2\) , \( a^{2} - 3\) , \( a^{3} - a^{2} - 3 a + 1\) , \( -126 a^{3} + 366 a^{2} - 63 a - 135\) , \( 107 a^{3} - 308 a^{2} + 47 a + 116\bigr] \)
|
| 12.2-d3
| \( \bigl[a\) , \( a^{2} - 2 a - 3\) , \( a^{3} - a^{2} - 3 a + 1\) , \( -a^{3} + a^{2} + 3 a + 1\) , \( -a\bigr] \)
|
| 12.2-d4
| \( \bigl[a\) , \( -a - 1\) , \( a^{3} - 5 a - 1\) , \( -1834 a^{3} + 2733 a^{2} + 7832 a - 7509\) , \( -7004 a^{3} + 10426 a^{2} + 29921 a - 28625\bigr] \)
|
Rank: \( 1 \)
\(\left(\begin{array}{rrrr}
1 & 6 & 3 & 2 \\
6 & 1 & 2 & 3 \\
3 & 2 & 1 & 6 \\
2 & 3 & 6 & 1
\end{array}\right)\)
