Elliptic curves in class 8.3-c over 4.4.13968.1
Isogeny class 8.3-c contains
4 curves linked by isogenies of
degrees dividing 4.
| Curve label |
Weierstrass Coefficients |
| 8.3-c1
| \( \bigl[\frac{1}{2} a^{2} + \frac{1}{2} a - 2\) , \( \frac{1}{2} a^{3} - a^{2} - \frac{5}{2} a + 2\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 2 a + 1\) , \( 2 a^{3} - 2 a^{2} - 16 a + 1\) , \( 2 a^{3} - 2 a^{2} - 15 a - 4\bigr] \)
|
| 8.3-c2
| \( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 2 a + 1\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - 1\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 3 a + 2\) , \( 2 a^{3} - \frac{1}{2} a^{2} - \frac{11}{2} a + 2\) , \( 3 a^{3} + 2 a^{2} - 12 a + 4\bigr] \)
|
| 8.3-c3
| \( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 2 a + 1\) , \( \frac{1}{2} a^{3} - a^{2} - \frac{5}{2} a + 3\) , \( \frac{1}{2} a^{3} - \frac{7}{2} a - 1\) , \( -\frac{33}{2} a^{3} + \frac{85}{2} a^{2} + 103 a - 180\) , \( \frac{157}{2} a^{3} - 179 a^{2} - \frac{953}{2} a + 770\bigr] \)
|
| 8.3-c4
| \( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 2 a + 1\) , \( \frac{1}{2} a^{3} - a^{2} - \frac{5}{2} a + 3\) , \( \frac{1}{2} a^{3} - \frac{7}{2} a - 1\) , \( a^{3} + \frac{5}{2} a^{2} - \frac{9}{2} a - 10\) , \( \frac{5}{2} a^{3} + 2 a^{2} - \frac{21}{2} a - 5\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrr}
1 & 4 & 4 & 2 \\
4 & 1 & 4 & 2 \\
4 & 4 & 1 & 2 \\
2 & 2 & 2 & 1
\end{array}\right)\)
