Elliptic curves in class 9.1-b over 4.4.15952.1
Isogeny class 9.1-b contains
8 curves linked by isogenies of
degrees dividing 12.
| Curve label |
Weierstrass Coefficients |
| 9.1-b1
| \( \bigl[a^{2} - 3\) , \( -a^{3} + a^{2} + 5 a - 3\) , \( a^{3} - 5 a - 1\) , \( -1001 a^{3} + 638 a^{2} + 5600 a - 1573\) , \( -10275 a^{3} + 6552 a^{2} + 57475 a - 16111\bigr] \)
|
| 9.1-b2
| \( \bigl[a^{2} - 3\) , \( -2 a^{3} + a^{2} + 10 a - 1\) , \( -a^{3} + a^{2} + 6 a - 1\) , \( -2 a^{3} - a^{2} + 6 a - 1\) , \( -2 a^{2} - 7 a - 8\bigr] \)
|
| 9.1-b3
| \( \bigl[a^{2} - 3\) , \( a^{3} - a^{2} - 5 a + 1\) , \( a\) , \( -24 a^{3} + 15 a^{2} + 133 a - 36\) , \( 42 a^{3} - 27 a^{2} - 235 a + 66\bigr] \)
|
| 9.1-b4
| \( \bigl[a^{2} - a - 2\) , \( -a^{3} + a^{2} + 5 a - 3\) , \( -a^{3} + a^{2} + 5 a - 2\) , \( 25 a^{3} - 49 a^{2} - 42 a + 6\) , \( -129 a^{3} + 261 a^{2} + 193 a - 26\bigr] \)
|
| 9.1-b5
| \( \bigl[a^{2} - a - 2\) , \( a^{3} - 7 a - 1\) , \( 1\) , \( -69 a^{3} + 46 a^{2} + 382 a - 112\) , \( -1020 a^{3} + 645 a^{2} + 5717 a - 1593\bigr] \)
|
| 9.1-b6
| \( \bigl[a^{3} - 6 a - 1\) , \( 0\) , \( -a^{3} + a^{2} + 5 a - 2\) , \( 7 a^{3} - a^{2} - 32 a + 8\) , \( 125 a^{3} + 281 a^{2} - 24\bigr] \)
|
| 9.1-b7
| \( \bigl[a^{3} - 5 a\) , \( a + 1\) , \( a^{2} - a - 3\) , \( 4 a^{3} + a^{2} - 21 a - 8\) , \( 2 a^{3} - 11 a - 7\bigr] \)
|
| 9.1-b8
| \( \bigl[a + 1\) , \( 2 a^{3} - a^{2} - 10 a + 2\) , \( 1\) , \( -225 a^{3} + 142 a^{2} + 1265 a - 355\) , \( -3465 a^{3} + 2207 a^{2} + 19387 a - 5434\bigr] \)
|
Rank: \( 1 \)
\(\left(\begin{array}{rrrrrrrr}
1 & 2 & 6 & 12 & 4 & 12 & 3 & 4 \\
2 & 1 & 3 & 6 & 2 & 6 & 6 & 2 \\
6 & 3 & 1 & 2 & 6 & 2 & 2 & 6 \\
12 & 6 & 2 & 1 & 12 & 4 & 4 & 3 \\
4 & 2 & 6 & 12 & 1 & 3 & 12 & 4 \\
12 & 6 & 2 & 4 & 3 & 1 & 4 & 12 \\
3 & 6 & 2 & 4 & 12 & 4 & 1 & 12 \\
4 & 2 & 6 & 3 & 4 & 12 & 12 & 1
\end{array}\right)\)
