Elliptic curves in class 4.1-b over 4.4.13824.1
Isogeny class 4.1-b contains
8 curves linked by isogenies of
degrees dividing 12.
| Curve label |
Weierstrass Coefficients |
| 4.1-b1
| \( \bigl[a^{3} + a^{2} - 4 a - 2\) , \( -a^{3} + a^{2} + 5 a - 4\) , \( a^{2} - 2\) , \( -49 a^{3} + 53 a^{2} + 232 a - 252\) , \( -280 a^{3} + 311 a^{2} + 1322 a - 1480\bigr] \)
|
| 4.1-b2
| \( \bigl[a^{3} + a^{2} - 4 a - 2\) , \( -a^{3} - a^{2} + 5 a + 2\) , \( a^{2} - 2\) , \( 87 a^{3} - 199 a^{2} - 102 a + 264\) , \( -1342 a^{3} + 2911 a^{2} + 1710 a - 3682\bigr] \)
|
| 4.1-b3
| \( \bigl[a^{3} - 3 a\) , \( a^{2} - 3\) , \( a^{3} - 4 a\) , \( -8 a^{2} + 7\) , \( -42 a^{2} + 51\bigr] \)
|
| 4.1-b4
| \( \bigl[a^{3} - 3 a\) , \( a^{2} - 3\) , \( 0\) , \( 2 a^{2} - 5\) , \( -1\bigr] \)
|
| 4.1-b5
| \( \bigl[0\) , \( a^{2} - 3\) , \( a\) , \( 1\) , \( -1\bigr] \)
|
| 4.1-b6
| \( \bigl[0\) , \( -a^{2} + 3\) , \( a^{3} - 3 a\) , \( 1\) , \( -a^{2} + 1\bigr] \)
|
| 4.1-b7
| \( \bigl[a\) , \( a^{2} - 3\) , \( a^{3} - 4 a\) , \( -a^{2} + 1\) , \( -2 a^{2} + 3\bigr] \)
|
| 4.1-b8
| \( \bigl[a\) , \( a^{2} - 3\) , \( 0\) , \( -10 a^{2} + 13\) , \( 15 a^{2} - 19\bigr] \)
|
Rank: \( 1 \)
\(\left(\begin{array}{rrrrrrrr}
1 & 3 & 2 & 2 & 2 & 6 & 6 & 6 \\
3 & 1 & 6 & 6 & 6 & 2 & 2 & 2 \\
2 & 6 & 1 & 4 & 4 & 12 & 3 & 12 \\
2 & 6 & 4 & 1 & 4 & 12 & 12 & 3 \\
2 & 6 & 4 & 4 & 1 & 3 & 12 & 12 \\
6 & 2 & 12 & 12 & 3 & 1 & 4 & 4 \\
6 & 2 & 3 & 12 & 12 & 4 & 1 & 4 \\
6 & 2 & 12 & 3 & 12 & 4 & 4 & 1
\end{array}\right)\)
