Elliptic curves in class 63.1-c over 4.4.19821.1
Isogeny class 63.1-c contains
4 curves linked by isogenies of
degrees dividing 6.
| Curve label |
Weierstrass Coefficients |
| 63.1-c1
| \( \bigl[a^{2} - a - 4\) , \( -\frac{1}{3} a^{3} - \frac{1}{3} a^{2} + 4 a + 1\) , \( -\frac{1}{3} a^{3} + \frac{2}{3} a^{2} + 3 a - 2\) , \( \frac{100}{3} a^{3} - \frac{131}{3} a^{2} - 140 a - 49\) , \( -\frac{970}{3} a^{3} + \frac{1037}{3} a^{2} + 1573 a + 490\bigr] \)
|
| 63.1-c2
| \( \bigl[1\) , \( -\frac{2}{3} a^{3} + \frac{1}{3} a^{2} + 5 a - 3\) , \( a^{2} - 4\) , \( -18 a^{3} + 23 a^{2} + 136 a - 151\) , \( 141 a^{3} - 190 a^{2} - 1061 a + 1213\bigr] \)
|
| 63.1-c3
| \( \bigl[1\) , \( \frac{2}{3} a^{3} - \frac{1}{3} a^{2} - 6 a + 1\) , \( 1\) , \( \frac{14}{3} a^{3} - \frac{1}{3} a^{2} - 38 a - 9\) , \( 4 a^{3} - 32 a - 9\bigr] \)
|
| 63.1-c4
| \( \bigl[1\) , \( \frac{2}{3} a^{3} - \frac{1}{3} a^{2} - 6 a + 1\) , \( 1\) , \( -12 a^{3} - 2 a^{2} + 92 a + 31\) , \( \frac{268}{3} a^{3} + \frac{34}{3} a^{2} - 700 a - 245\bigr] \)
|
Rank: \( 1 \)
\(\left(\begin{array}{rrrr}
1 & 2 & 6 & 3 \\
2 & 1 & 3 & 6 \\
6 & 3 & 1 & 2 \\
3 & 6 & 2 & 1
\end{array}\right)\)
