Elliptic curves in class 16.1-d over 4.4.13888.1
Isogeny class 16.1-d contains
4 curves linked by isogenies of
degrees dividing 6.
| Curve label |
Weierstrass Coefficients |
| 16.1-d1
| \( \bigl[a^{2} - a - 3\) , \( -\frac{1}{3} a^{3} - \frac{1}{3} a^{2} + \frac{7}{3} a + 3\) , \( \frac{1}{3} a^{3} - \frac{2}{3} a^{2} - \frac{4}{3} a + 1\) , \( -\frac{128}{3} a^{3} + \frac{367}{3} a^{2} + \frac{563}{3} a - 414\) , \( -\frac{1088}{3} a^{3} + \frac{3157}{3} a^{2} + \frac{4763}{3} a - 3605\bigr] \)
|
| 16.1-d2
| \( \bigl[\frac{1}{3} a^{3} + \frac{1}{3} a^{2} - \frac{7}{3} a - 2\) , \( -\frac{1}{3} a^{3} + \frac{5}{3} a^{2} - \frac{2}{3} a - 4\) , \( \frac{1}{3} a^{3} + \frac{1}{3} a^{2} - \frac{7}{3} a - 2\) , \( -3 a^{3} + 10 a^{2} + 2 a - 22\) , \( \frac{40}{3} a^{3} - \frac{164}{3} a^{2} + \frac{44}{3} a + 55\bigr] \)
|
| 16.1-d3
| \( \bigl[\frac{1}{3} a^{3} + \frac{1}{3} a^{2} - \frac{7}{3} a - 2\) , \( \frac{1}{3} a^{3} - \frac{5}{3} a^{2} - \frac{4}{3} a + 6\) , \( 0\) , \( -4 a^{3} + 12 a^{2} + 12 a - 52\) , \( -\frac{70}{3} a^{3} + \frac{206}{3} a^{2} + \frac{232}{3} a - 284\bigr] \)
|
| 16.1-d4
| \( \bigl[\frac{1}{3} a^{3} + \frac{1}{3} a^{2} - \frac{7}{3} a - 2\) , \( \frac{1}{3} a^{3} - \frac{5}{3} a^{2} - \frac{4}{3} a + 6\) , \( 0\) , \( a^{3} - 3 a^{2} - 3 a + 13\) , \( 0\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrr}
1 & 2 & 6 & 3 \\
2 & 1 & 3 & 6 \\
6 & 3 & 1 & 2 \\
3 & 6 & 2 & 1
\end{array}\right)\)
