Elliptic curves in class 3.1-b over 4.4.15952.1
Isogeny class 3.1-b contains
4 curves linked by isogenies of
degrees dividing 4.
| Curve label |
Weierstrass Coefficients |
| 3.1-b1
| \( \bigl[a^{2} - 3\) , \( -a^{3} + 6 a + 1\) , \( 1\) , \( -7 a^{3} + 3 a^{2} + 40 a - 3\) , \( -35 a^{3} + 22 a^{2} + 196 a - 53\bigr] \)
|
| 3.1-b2
| \( \bigl[a^{2} - 3\) , \( -a^{2} + 2 a + 2\) , \( a^{3} - 6 a\) , \( 26 a^{3} + 7 a^{2} - 158 a - 91\) , \( -10 a^{3} - 4 a^{2} + 61 a + 35\bigr] \)
|
| 3.1-b3
| \( \bigl[-a^{3} + a^{2} + 6 a - 2\) , \( a^{3} - a^{2} - 5 a + 2\) , \( a\) , \( 7 a^{3} - 3 a^{2} - 39 a + 7\) , \( -a^{3} + a^{2} + 8 a\bigr] \)
|
| 3.1-b4
| \( \bigl[a + 1\) , \( -2 a^{3} + a^{2} + 12 a - 2\) , \( a\) , \( 4 a^{3} - 6 a^{2} - 28 a + 10\) , \( -4 a^{3} + 5 a^{2} + 28 a - 7\bigr] \)
|
Rank: \( 1 \)
\(\left(\begin{array}{rrrr}
1 & 2 & 4 & 4 \\
2 & 1 & 2 & 2 \\
4 & 2 & 1 & 4 \\
4 & 2 & 4 & 1
\end{array}\right)\)
