Elliptic curves in class 16.1-c over 4.4.13888.1
Isogeny class 16.1-c contains
4 curves linked by isogenies of
degrees dividing 6.
| Curve label |
Weierstrass Coefficients |
| 16.1-c1
| \( \bigl[\frac{1}{3} a^{3} + \frac{1}{3} a^{2} - \frac{7}{3} a - 2\) , \( -\frac{1}{3} a^{3} - \frac{1}{3} a^{2} + \frac{7}{3} a + 3\) , \( \frac{1}{3} a^{3} - \frac{2}{3} a^{2} - \frac{4}{3} a + 1\) , \( -\frac{37}{3} a^{3} + \frac{98}{3} a^{2} + \frac{175}{3} a - 104\) , \( -\frac{149}{3} a^{3} + \frac{424}{3} a^{2} + \frac{665}{3} a - 477\bigr] \)
|
| 16.1-c2
| \( \bigl[\frac{1}{3} a^{3} + \frac{1}{3} a^{2} - \frac{7}{3} a - 2\) , \( -\frac{1}{3} a^{3} - \frac{1}{3} a^{2} + \frac{7}{3} a + 3\) , \( \frac{1}{3} a^{3} - \frac{2}{3} a^{2} - \frac{4}{3} a + 1\) , \( -\frac{2}{3} a^{3} - \frac{2}{3} a^{2} + \frac{20}{3} a + 11\) , \( -\frac{11}{3} a^{3} + \frac{25}{3} a^{2} + \frac{59}{3} a - 21\bigr] \)
|
| 16.1-c3
| \( \bigl[\frac{1}{3} a^{3} - \frac{2}{3} a^{2} - \frac{4}{3} a + 1\) , \( -a^{2} + 2 a + 3\) , \( \frac{1}{3} a^{3} - \frac{2}{3} a^{2} - \frac{4}{3} a + 1\) , \( a^{3} - 2 a^{2} - 6 a - 4\) , \( -\frac{53}{3} a^{3} + \frac{25}{3} a^{2} + \frac{416}{3} a + 105\bigr] \)
|
| 16.1-c4
| \( \bigl[\frac{1}{3} a^{3} - \frac{2}{3} a^{2} - \frac{4}{3} a + 1\) , \( \frac{1}{3} a^{3} - \frac{5}{3} a^{2} - \frac{4}{3} a + 5\) , \( \frac{1}{3} a^{3} - \frac{2}{3} a^{2} - \frac{4}{3} a + 1\) , \( \frac{4}{3} a^{3} - \frac{5}{3} a^{2} - \frac{16}{3} a + 5\) , \( \frac{8}{3} a^{3} + \frac{5}{3} a^{2} - \frac{23}{3} a - 2\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrr}
1 & 2 & 3 & 6 \\
2 & 1 & 6 & 3 \\
3 & 6 & 1 & 2 \\
6 & 3 & 2 & 1
\end{array}\right)\)
