Elliptic curves in class 28.1-b over 4.4.7168.1
Isogeny class 28.1-b contains
12 curves linked by isogenies of
degrees dividing 24.
| Curve label |
Weierstrass Coefficients |
| 28.1-b1
| \( \bigl[a^{2} - 3\) , \( -1\) , \( a^{2} - 3\) , \( 2 a^{2} - 10\) , \( -a^{2} + 4\bigr] \)
|
| 28.1-b2
| \( \bigl[a^{2} - 3\) , \( -a^{2} + 4\) , \( 0\) , \( -34 a^{2} + 49\) , \( -133 a^{2} + 196\bigr] \)
|
| 28.1-b3
| \( \bigl[a^{2} + a - 2\) , \( -a^{3} + 5 a\) , \( a^{2} + a - 2\) , \( -79 a^{3} + 84 a^{2} + 327 a - 416\) , \( -895 a^{3} - 276 a^{2} + 2735 a - 1336\bigr] \)
|
| 28.1-b4
| \( \bigl[a^{2} + a - 2\) , \( -a^{3} + 5 a\) , \( a^{2} + a - 2\) , \( -19 a^{3} + 29 a^{2} + 87 a - 121\) , \( 141 a^{3} - 119 a^{2} - 573 a + 629\bigr] \)
|
| 28.1-b5
| \( \bigl[a^{2} + a - 2\) , \( -a^{3} + 5 a\) , \( a^{3} - 3 a\) , \( 51937 a^{3} - 109122 a^{2} - 82363 a + 173047\) , \( -4497906 a^{3} + 9450115 a^{2} + 7132713 a - 14985873\bigr] \)
|
| 28.1-b6
| \( \bigl[a^{2} + a - 2\) , \( -a^{3} + 5 a\) , \( a^{3} - 4 a + 1\) , \( -48 a^{3} - 56 a^{2} + 114 a + 42\) , \( 168 a^{3} + 482 a^{2} - 162 a - 910\bigr] \)
|
| 28.1-b7
| \( \bigl[0\) , \( a^{2} - a - 2\) , \( a + 1\) , \( 34 a^{3} + 24 a^{2} - 216 a - 242\) , \( 344 a^{3} + 305 a^{2} - 1941 a - 2241\bigr] \)
|
| 28.1-b8
| \( \bigl[0\) , \( a^{2} - a - 2\) , \( a + 1\) , \( -6 a^{3} - 6 a^{2} + 24 a + 28\) , \( -2 a^{3} - 2 a^{2} + 7 a + 8\bigr] \)
|
| 28.1-b9
| \( \bigl[a + 1\) , \( a^{2} - a - 2\) , \( a^{2} + a - 2\) , \( 3879 a^{3} + 4939 a^{2} - 17012 a - 21585\) , \( 245032 a^{3} + 308773 a^{2} - 1081264 a - 1362224\bigr] \)
|
| 28.1-b10
| \( \bigl[a + 1\) , \( a^{2} - a - 2\) , \( a^{2} + a - 2\) , \( 4 a^{3} - 6 a^{2} - 37 a - 30\) , \( 859 a^{3} + 1104 a^{2} - 3731 a - 4735\bigr] \)
|
| 28.1-b11
| \( \bigl[a + 1\) , \( a^{2} - 2\) , \( a^{2} + a - 2\) , \( -3880 a^{3} + 4939 a^{2} + 17013 a - 21585\) , \( -245033 a^{3} + 308773 a^{2} + 1081266 a - 1362224\bigr] \)
|
| 28.1-b12
| \( \bigl[a + 1\) , \( a^{2} - 2\) , \( a^{2} + a - 2\) , \( -5 a^{3} - 6 a^{2} + 38 a - 30\) , \( -860 a^{3} + 1104 a^{2} + 3733 a - 4735\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrrrrrrrrrr}
1 & 3 & 6 & 2 & 6 & 2 & 6 & 2 & 12 & 4 & 12 & 4 \\
3 & 1 & 2 & 6 & 2 & 6 & 2 & 6 & 4 & 12 & 4 & 12 \\
6 & 2 & 1 & 3 & 4 & 12 & 4 & 12 & 8 & 24 & 8 & 24 \\
2 & 6 & 3 & 1 & 12 & 4 & 12 & 4 & 24 & 8 & 24 & 8 \\
6 & 2 & 4 & 12 & 1 & 3 & 4 & 12 & 2 & 6 & 2 & 6 \\
2 & 6 & 12 & 4 & 3 & 1 & 12 & 4 & 6 & 2 & 6 & 2 \\
6 & 2 & 4 & 12 & 4 & 12 & 1 & 3 & 8 & 24 & 8 & 24 \\
2 & 6 & 12 & 4 & 12 & 4 & 3 & 1 & 24 & 8 & 24 & 8 \\
12 & 4 & 8 & 24 & 2 & 6 & 8 & 24 & 1 & 3 & 4 & 12 \\
4 & 12 & 24 & 8 & 6 & 2 & 24 & 8 & 3 & 1 & 12 & 4 \\
12 & 4 & 8 & 24 & 2 & 6 & 8 & 24 & 4 & 12 & 1 & 3 \\
4 & 12 & 24 & 8 & 6 & 2 & 24 & 8 & 12 & 4 & 3 & 1
\end{array}\right)\)
