Elliptic curves in class 6.1-b over 4.4.13068.1
Isogeny class 6.1-b contains
8 curves linked by isogenies of
degrees dividing 16.
| Curve label |
Weierstrass Coefficients |
| 6.1-b1
| \( \bigl[-a^{3} + 2 a^{2} + 4 a - 2\) , \( a^{3} - a^{2} - 7 a - 1\) , \( -a^{3} + 2 a^{2} + 4 a - 2\) , \( -16 a^{3} + 16 a^{2} + 112 a - 34\) , \( -86 a^{3} + 86 a^{2} + 602 a - 206\bigr] \)
|
| 6.1-b2
| \( \bigl[-a^{3} + 2 a^{2} + 4 a - 2\) , \( a^{3} - a^{2} - 7 a - 1\) , \( -a^{3} + 2 a^{2} + 4 a - 2\) , \( -a^{3} + a^{2} + 7 a + 1\) , \( -2 a^{3} + 2 a^{2} + 14 a - 6\bigr] \)
|
| 6.1-b3
| \( \bigl[-a^{3} + 2 a^{2} + 4 a - 2\) , \( 1\) , \( a^{3} - a^{2} - 5 a - 1\) , \( a^{3} - a^{2} - 7 a + 4\) , \( -3 a^{3} + 3 a^{2} + 21 a + 12\bigr] \)
|
| 6.1-b4
| \( \bigl[a^{3} - a^{2} - 6 a - 1\) , \( -2 a^{3} + 3 a^{2} + 10 a - 2\) , \( a + 1\) , \( 76 a^{3} - 152 a^{2} - 260 a - 77\) , \( -552 a^{3} + 1306 a^{2} + 1267 a + 210\bigr] \)
|
| 6.1-b5
| \( \bigl[a^{3} - a^{2} - 6 a - 1\) , \( -a^{2} + 3 a + 4\) , \( a\) , \( -110 a^{3} + 305 a^{2} + 108 a - 47\) , \( 4406 a^{3} - 12448 a^{2} - 3727 a + 2425\bigr] \)
|
| 6.1-b6
| \( \bigl[a\) , \( a^{3} - 2 a^{2} - 3 a + 1\) , \( a^{3} - a^{2} - 6 a\) , \( -120 a^{3} + 196 a^{2} + 567 a - 337\) , \( 1290 a^{3} - 2044 a^{2} - 6434 a + 2892\bigr] \)
|
| 6.1-b7
| \( \bigl[a\) , \( a^{3} - 2 a^{2} - 3 a + 1\) , \( a^{3} - a^{2} - 6 a\) , \( -150 a^{3} + 221 a^{2} + 747 a - 272\) , \( 1299 a^{3} - 1958 a^{2} - 6605 a + 2344\bigr] \)
|
| 6.1-b8
| \( \bigl[a\) , \( a^{3} - 2 a^{2} - 3 a + 1\) , \( a^{3} - a^{2} - 6 a\) , \( -10 a^{3} + 16 a^{2} + 47 a - 17\) , \( 14 a^{3} - 22 a^{2} - 70 a + 24\bigr] \)
|
Rank: \( 1 \)
\(\left(\begin{array}{rrrrrrrr}
1 & 2 & 8 & 16 & 4 & 16 & 8 & 4 \\
2 & 1 & 4 & 8 & 2 & 8 & 4 & 2 \\
8 & 4 & 1 & 8 & 8 & 8 & 4 & 2 \\
16 & 8 & 8 & 1 & 16 & 4 & 2 & 4 \\
4 & 2 & 8 & 16 & 1 & 16 & 8 & 4 \\
16 & 8 & 8 & 4 & 16 & 1 & 2 & 4 \\
8 & 4 & 4 & 2 & 8 & 2 & 1 & 2 \\
4 & 2 & 2 & 4 & 4 & 4 & 2 & 1
\end{array}\right)\)
