Elliptic curves in class 5.1-b over 4.4.11324.1
Isogeny class 5.1-b contains
4 curves linked by isogenies of
degrees dividing 4.
| Curve label |
Weierstrass Coefficients |
| 5.1-b1
| \( \bigl[a^{3} + a^{2} - 3 a - 3\) , \( -a - 1\) , \( 1\) , \( 3 a^{3} + 2 a^{2} - 11 a - 3\) , \( 4 a^{3} + 2 a^{2} - 16 a - 6\bigr] \)
|
| 5.1-b2
| \( \bigl[a^{3} - 3 a + 1\) , \( a^{3} + a^{2} - 3 a - 4\) , \( a^{2} - 2\) , \( 4 a^{3} + 10 a^{2} - 10 a - 25\) , \( -254 a^{3} - 332 a^{2} + 552 a + 284\bigr] \)
|
| 5.1-b3
| \( \bigl[a + 1\) , \( a^{3} + a^{2} - 4 a - 3\) , \( a^{2} + a - 3\) , \( -9 a^{3} + 13 a^{2} + 43 a - 50\) , \( -22 a^{3} + 32 a^{2} + 101 a - 130\bigr] \)
|
| 5.1-b4
| \( \bigl[a + 1\) , \( a^{3} + a^{2} - 4 a - 2\) , \( a^{2} - 2\) , \( 33 a^{3} + 7 a^{2} - 155 a - 54\) , \( 137 a^{3} + 25 a^{2} - 654 a - 231\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrr}
1 & 4 & 4 & 2 \\
4 & 1 & 4 & 2 \\
4 & 4 & 1 & 2 \\
2 & 2 & 2 & 1
\end{array}\right)\)
