Elliptic curves in class 16.2-d over 4.4.13068.1
Isogeny class 16.2-d contains
8 curves linked by isogenies of
degrees dividing 12.
| Curve label |
Weierstrass Coefficients |
| 16.2-d1
| \( \bigl[a^{2} - 2 a - 3\) , \( -a^{3} + a^{2} + 7 a + 1\) , \( -a^{3} + 2 a^{2} + 5 a - 2\) , \( 51 a^{3} - 36 a^{2} - 321 a - 159\) , \( -238 a^{3} + 154 a^{2} + 1464 a + 713\bigr] \)
|
| 16.2-d2
| \( \bigl[a^{2} - a - 2\) , \( a^{3} - a^{2} - 6 a - 1\) , \( -a^{3} + 2 a^{2} + 5 a - 2\) , \( 5 a^{3} + 5 a^{2} - 12 a - 8\) , \( 5 a^{3} + 8 a^{2} - 7 a - 9\bigr] \)
|
| 16.2-d3
| \( \bigl[a^{2} - a - 2\) , \( a^{3} - a^{2} - 6 a - 1\) , \( -a^{3} + 2 a^{2} + 5 a - 2\) , \( 11 a^{3} - 31 a^{2} - 12 a + 4\) , \( -149 a^{3} + 418 a^{2} + 129 a - 83\bigr] \)
|
| 16.2-d4
| \( \bigl[a^{2} - a - 2\) , \( a^{3} - a^{2} - 6 a - 1\) , \( -a^{3} + 2 a^{2} + 5 a - 2\) , \( 16 a^{3} - 46 a^{2} - 12 a + 9\) , \( -78 a^{3} + 219 a^{2} + 70 a - 44\bigr] \)
|
| 16.2-d5
| \( \bigl[a^{2} - a - 2\) , \( -a^{2} + 3 a + 3\) , \( -a^{3} + 2 a^{2} + 4 a - 1\) , \( -56 a^{3} + 86 a^{2} + 293 a - 95\) , \( 286 a^{3} - 443 a^{2} - 1469 a + 524\bigr] \)
|
| 16.2-d6
| \( \bigl[a^{2} - a - 2\) , \( -a^{2} + 3 a + 3\) , \( -a^{3} + 2 a^{2} + 4 a - 1\) , \( -36 a^{3} + 56 a^{2} + 188 a - 65\) , \( 515 a^{3} - 795 a^{2} - 2654 a + 923\bigr] \)
|
| 16.2-d7
| \( \bigl[a^{2} - a - 2\) , \( -a^{2} + 3 a + 3\) , \( -a^{3} + 2 a^{2} + 4 a - 1\) , \( -30 a^{3} + 20 a^{2} + 188 a + 91\) , \( -47 a^{3} + 29 a^{2} + 290 a + 141\bigr] \)
|
| 16.2-d8
| \( \bigl[-a^{3} + 2 a^{2} + 5 a - 2\) , \( -a^{3} + a^{2} + 7 a + 1\) , \( a^{2} - 2 a - 3\) , \( -15 a^{2} - 36 a - 18\) , \( 48 a^{3} + 36 a^{2} - 134 a - 77\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrrrrrr}
1 & 12 & 12 & 6 & 2 & 4 & 4 & 3 \\
12 & 1 & 4 & 2 & 6 & 12 & 3 & 4 \\
12 & 4 & 1 & 2 & 6 & 3 & 12 & 4 \\
6 & 2 & 2 & 1 & 3 & 6 & 6 & 2 \\
2 & 6 & 6 & 3 & 1 & 2 & 2 & 6 \\
4 & 12 & 3 & 6 & 2 & 1 & 4 & 12 \\
4 & 3 & 12 & 6 & 2 & 4 & 1 & 12 \\
3 & 4 & 4 & 2 & 6 & 12 & 12 & 1
\end{array}\right)\)
