Elliptic curves in class 8.1-b over 4.4.13068.1
Isogeny class 8.1-b contains
6 curves linked by isogenies of
degrees dividing 18.
| Curve label |
Weierstrass Coefficients |
| 8.1-b1
| \( \bigl[a^{2} - 2 a - 2\) , \( -a - 1\) , \( a^{3} - a^{2} - 6 a - 1\) , \( 107 a^{3} - 300 a^{2} - 95 a + 56\) , \( -1259 a^{3} + 3556 a^{2} + 1067 a - 692\bigr] \)
|
| 8.1-b2
| \( \bigl[a^{2} - 2 a - 2\) , \( -a - 1\) , \( a^{3} - a^{2} - 6 a - 1\) , \( 1277 a^{3} - 3605 a^{2} - 1085 a + 696\) , \( 66818 a^{3} - 188697 a^{2} - 56715 a + 36628\bigr] \)
|
| 8.1-b3
| \( \bigl[a^{2} - 2 a - 2\) , \( -a - 1\) , \( a^{3} - a^{2} - 6 a - 1\) , \( 8597 a^{3} - 24280 a^{2} - 7285 a + 4696\) , \( -1102543 a^{3} + 3113650 a^{2} + 935779 a - 604426\bigr] \)
|
| 8.1-b4
| \( \bigl[-a^{3} + 2 a^{2} + 5 a - 1\) , \( -a^{3} + 2 a^{2} + 3 a - 1\) , \( -a^{3} + 2 a^{2} + 5 a - 2\) , \( -134 a^{3} - 329 a^{2} - 288 a - 225\) , \( 5161 a^{3} + 11385 a^{2} + 3585 a - 1\bigr] \)
|
| 8.1-b5
| \( \bigl[-a^{3} + 2 a^{2} + 5 a - 1\) , \( -a^{3} + 2 a^{2} + 3 a - 1\) , \( -a^{3} + 2 a^{2} + 5 a - 2\) , \( -19 a^{3} - 49 a^{2} - 53 a - 30\) , \( -348 a^{3} - 709 a^{2} - 154 a - 16\bigr] \)
|
| 8.1-b6
| \( \bigl[-a^{3} + 2 a^{2} + 5 a - 1\) , \( -a^{3} + 2 a^{2} + 3 a - 1\) , \( -a^{3} + 2 a^{2} + 5 a - 2\) , \( -4 a^{3} + a^{2} + 2 a - 5\) , \( 3 a^{3} + 15 a^{2} + 7 a - 1\bigr] \)
|
Rank: \( 1 \)
\(\left(\begin{array}{rrrrrr}
1 & 3 & 3 & 6 & 6 & 2 \\
3 & 1 & 9 & 18 & 2 & 6 \\
3 & 9 & 1 & 2 & 18 & 6 \\
6 & 18 & 2 & 1 & 9 & 3 \\
6 & 2 & 18 & 9 & 1 & 3 \\
2 & 6 & 6 & 3 & 3 & 1
\end{array}\right)\)
