Elliptic curves in class 45.2-e over 4.4.4525.1
Isogeny class 45.2-e contains
4 curves linked by isogenies of
degrees dividing 6.
| Curve label |
Weierstrass Coefficients |
| 45.2-e1
| \( \bigl[\frac{1}{3} a^{3} + \frac{2}{3} a^{2} - \frac{4}{3} a - 4\) , \( -\frac{1}{3} a^{3} + \frac{1}{3} a^{2} + \frac{4}{3} a + 1\) , \( \frac{1}{3} a^{3} + \frac{2}{3} a^{2} - \frac{7}{3} a - 3\) , \( -\frac{5}{3} a^{3} + \frac{11}{3} a^{2} + \frac{8}{3} a - 3\) , \( -\frac{10}{3} a^{3} + \frac{28}{3} a^{2} + \frac{10}{3} a - 12\bigr] \)
|
| 45.2-e2
| \( \bigl[a^{2} - 4\) , \( \frac{1}{3} a^{3} + \frac{2}{3} a^{2} - \frac{7}{3} a - 4\) , \( \frac{1}{3} a^{3} - \frac{1}{3} a^{2} - \frac{1}{3} a\) , \( -\frac{1}{3} a^{3} + \frac{1}{3} a^{2} + \frac{1}{3} a - 3\) , \( \frac{1}{3} a^{3} - \frac{10}{3} a^{2} - \frac{7}{3} a + 9\bigr] \)
|
| 45.2-e3
| \( \bigl[\frac{1}{3} a^{3} + \frac{2}{3} a^{2} - \frac{7}{3} a - 3\) , \( a^{2} - 5\) , \( a + 1\) , \( \frac{1}{3} a^{3} - \frac{13}{3} a^{2} + \frac{5}{3} a + 10\) , \( \frac{11}{3} a^{3} + \frac{34}{3} a^{2} - \frac{32}{3} a - 21\bigr] \)
|
| 45.2-e4
| \( \bigl[\frac{1}{3} a^{3} - \frac{1}{3} a^{2} - \frac{1}{3} a\) , \( a^{2} - 2 a - 5\) , \( a^{2} - 4\) , \( \frac{13}{3} a^{3} + \frac{23}{3} a^{2} - \frac{106}{3} a - 53\) , \( -\frac{46}{3} a^{3} - \frac{29}{3} a^{2} + \frac{289}{3} a + 114\bigr] \)
|
Rank: \( 1 \)
\(\left(\begin{array}{rrrr}
1 & 3 & 2 & 6 \\
3 & 1 & 6 & 2 \\
2 & 6 & 1 & 3 \\
6 & 2 & 3 & 1
\end{array}\right)\)
