Elliptic curves in class 5.1-b over 4.4.19025.1
Isogeny class 5.1-b contains
4 curves linked by isogenies of
degrees dividing 4.
| Curve label |
Weierstrass Coefficients |
| 5.1-b1
| \( \bigl[\frac{1}{2} a^{2} - \frac{1}{2} a - 4\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - 3\) , \( a\) , \( -2 a^{3} - 3 a^{2} + 12 a + 18\) , \( -\frac{17}{2} a^{3} - \frac{29}{2} a^{2} + 59 a + 101\bigr] \)
|
| 5.1-b2
| \( \bigl[\frac{1}{2} a^{2} - \frac{1}{2} a - 4\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - 3\) , \( a\) , \( -37 a^{3} - \frac{121}{2} a^{2} + \frac{519}{2} a + 438\) , \( -\frac{1093}{2} a^{3} - \frac{1711}{2} a^{2} + 4049 a + 6754\bigr] \)
|
| 5.1-b3
| \( \bigl[\frac{1}{2} a^{2} - \frac{1}{2} a - 4\) , \( -a + 1\) , \( \frac{1}{2} a^{3} - \frac{7}{2} a - 4\) , \( -5 a^{3} + 19 a^{2} + 31 a - 127\) , \( \frac{85}{2} a^{3} - \frac{321}{2} a^{2} - 276 a + 1084\bigr] \)
|
| 5.1-b4
| \( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 4 a + 1\) , \( -\frac{1}{2} a^{3} + \frac{1}{2} a^{2} + 4 a + 1\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 3 a + 1\) , \( -3 a^{3} + 4 a^{2} + 26 a - 17\) , \( -a^{3} - 4 a^{2} + 15 a + 32\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrr}
1 & 2 & 2 & 2 \\
2 & 1 & 4 & 4 \\
2 & 4 & 1 & 4 \\
2 & 4 & 4 & 1
\end{array}\right)\)
