Elliptic curves in class 49.4-b over 4.4.4205.1
Isogeny class 49.4-b contains
4 curves linked by isogenies of
degrees dividing 15.
| Curve label |
Weierstrass Coefficients |
| 49.4-b1
| \( \bigl[a^{3} - a^{2} - 5 a - 1\) , \( 2 a^{3} - 3 a^{2} - 8 a + 1\) , \( a^{3} - a^{2} - 5 a\) , \( -18 a^{3} + 32 a^{2} + 67 a - 43\) , \( -155 a^{3} + 223 a^{2} + 667 a - 71\bigr] \)
|
| 49.4-b2
| \( \bigl[a^{3} - a^{2} - 5 a - 1\) , \( 2 a^{3} - 3 a^{2} - 8 a + 1\) , \( a^{3} - a^{2} - 5 a\) , \( 2 a^{3} - 3 a^{2} - 8 a + 2\) , \( 2 a^{3} - 2 a^{2} - 10 a - 4\bigr] \)
|
| 49.4-b3
| \( \bigl[-a^{3} + 2 a^{2} + 4 a - 1\) , \( -a + 1\) , \( a + 1\) , \( -17 a^{3} + 30 a^{2} + 61 a - 40\) , \( -661 a^{3} + 1087 a^{2} + 2599 a - 1002\bigr] \)
|
| 49.4-b4
| \( \bigl[-a^{3} + 2 a^{2} + 4 a - 1\) , \( -a + 1\) , \( a + 1\) , \( 3 a^{3} - 5 a^{2} - 14 a + 5\) , \( 26 a^{3} - 43 a^{2} - 103 a + 40\bigr] \)
|
Rank: \( 1 \)
\(\left(\begin{array}{rrrr}
1 & 3 & 5 & 15 \\
3 & 1 & 15 & 5 \\
5 & 15 & 1 & 3 \\
15 & 5 & 3 & 1
\end{array}\right)\)
