Elliptic curves in class 2.1-b over 5.5.81509.1
Isogeny class 2.1-b contains
4 curves linked by isogenies of
degrees dividing 6.
| Curve label |
Weierstrass Coefficients |
| 2.1-b1
| \( \bigl[a^{2} + a - 1\) , \( -a^{4} + a^{3} + 4 a^{2} - 2 a - 3\) , \( a^{2} - 2\) , \( 19 a^{4} + 5 a^{3} - 89 a^{2} - 53 a + 31\) , \( -71 a^{4} - 15 a^{3} + 338 a^{2} + 199 a - 115\bigr] \)
|
| 2.1-b2
| \( \bigl[a^{4} - 5 a^{2} + 3\) , \( a^{4} - a^{3} - 4 a^{2} + 3 a + 2\) , \( a^{2} + a - 1\) , \( -2 a^{4} + 7 a^{3} - 3 a^{2} - 9 a + 9\) , \( 6 a^{4} - 15 a^{3} - 5 a^{2} + 20 a - 4\bigr] \)
|
| 2.1-b3
| \( \bigl[a^{2} - 1\) , \( -a^{4} + 2 a^{3} + 2 a^{2} - 6 a + 2\) , \( 1\) , \( -17 a^{4} + 14 a^{3} + 82 a^{2} - 28 a - 74\) , \( 45 a^{4} - 27 a^{3} - 237 a^{2} + 41 a + 250\bigr] \)
|
| 2.1-b4
| \( \bigl[1\) , \( -a^{2} - a + 2\) , \( a^{4} - a^{3} - 4 a^{2} + 3 a + 3\) , \( 13 a^{4} + 2 a^{3} - 58 a^{2} - 36 a + 18\) , \( -63 a^{4} + 24 a^{3} + 242 a^{2} + 91 a - 70\bigr] \)
|
Rank: \( 1 \)
\(\left(\begin{array}{rrrr}
1 & 3 & 6 & 2 \\
3 & 1 & 2 & 6 \\
6 & 2 & 1 & 3 \\
2 & 6 & 3 & 1
\end{array}\right)\)
