Elliptic curves in class 19.1-b over 4.4.12400.1
Isogeny class 19.1-b contains
4 curves linked by isogenies of
degrees dividing 6.
| Curve label |
Weierstrass Coefficients |
| 19.1-b1
| \( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{7}{2} a - \frac{7}{2}\) , \( -\frac{1}{2} a^{3} + \frac{5}{2} a - 1\) , \( \frac{1}{2} a^{3} - \frac{5}{2} a + 1\) , \( -\frac{1}{2} a^{3} - a^{2} + \frac{5}{2} a + 6\) , \( \frac{1}{2} a^{2} + a - \frac{7}{2}\bigr] \)
|
| 19.1-b2
| \( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - \frac{5}{2}\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{7}{2} a - \frac{9}{2}\) , \( \frac{1}{2} a^{3} - \frac{7}{2} a + 1\) , \( 10 a^{3} - \frac{53}{2} a^{2} - 19 a + \frac{139}{2}\) , \( 142 a^{3} - 404 a^{2} - 492 a + 1433\bigr] \)
|
| 19.1-b3
| \( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - \frac{5}{2}\) , \( \frac{1}{2} a^{3} - \frac{9}{2} a - 1\) , \( \frac{1}{2} a^{2} + a - \frac{7}{2}\) , \( \frac{37}{2} a^{3} + 52 a^{2} - \frac{137}{2} a - 189\) , \( 50 a^{3} + \frac{289}{2} a^{2} - 188 a - \frac{1097}{2}\bigr] \)
|
| 19.1-b4
| \( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - \frac{5}{2}\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{9}{2} a + \frac{9}{2}\) , \( \frac{1}{2} a^{3} - \frac{7}{2} a\) , \( -a^{3} + 5 a^{2} + 20 a - 53\) , \( -\frac{59}{2} a^{3} + 64 a^{2} + \frac{483}{2} a - 496\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrr}
1 & 2 & 6 & 3 \\
2 & 1 & 3 & 6 \\
6 & 3 & 1 & 2 \\
3 & 6 & 2 & 1
\end{array}\right)\)
