Elliptic curves in class 12.1-d over 4.4.8112.1
Isogeny class 12.1-d contains
3 curves linked by isogenies of
degrees dividing 9.
| Curve label |
Weierstrass Coefficients |
| 12.1-d1
| \( \bigl[a^{2} - 2\) , \( a^{3} + a^{2} - 4 a - 2\) , \( a + 1\) , \( 33 a^{3} + 29 a^{2} - 142 a - 127\) , \( 313 a^{3} - 1350 a^{2} + 645 a + 1667\bigr] \)
|
| 12.1-d2
| \( \bigl[a^{2} - 2\) , \( a^{3} + a^{2} - 4 a - 2\) , \( a + 1\) , \( -2 a^{3} - a^{2} + 8 a + 8\) , \( -20 a^{3} + 43 a^{2} + 12 a - 31\bigr] \)
|
| 12.1-d3
| \( \bigl[a^{2} + a - 2\) , \( -a^{3} + 4 a + 1\) , \( a^{3} - 3 a + 1\) , \( -7 a^{3} + 5 a^{2} + 30 a - 21\) , \( -19 a^{3} + 16 a^{2} + 82 a - 69\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrr}
1 & 3 & 9 \\
3 & 1 & 3 \\
9 & 3 & 1
\end{array}\right)\)
