Elliptic curves in class 45.3-e over 4.4.4525.1
Isogeny class 45.3-e contains
4 curves linked by isogenies of
degrees dividing 6.
| Curve label |
Weierstrass Coefficients |
| 45.3-e1
| \( \bigl[\frac{1}{3} a^{3} + \frac{2}{3} a^{2} - \frac{7}{3} a - 4\) , \( -\frac{1}{3} a^{3} + \frac{1}{3} a^{2} + \frac{7}{3} a\) , \( 1\) , \( -\frac{17}{3} a^{3} + \frac{14}{3} a^{2} + \frac{95}{3} a - 5\) , \( 4 a^{3} - 17 a^{2} - 13 a + 81\bigr] \)
|
| 45.3-e2
| \( \bigl[\frac{1}{3} a^{3} + \frac{2}{3} a^{2} - \frac{7}{3} a - 4\) , \( -\frac{1}{3} a^{3} + \frac{1}{3} a^{2} + \frac{7}{3} a\) , \( 1\) , \( -\frac{7}{3} a^{3} + \frac{4}{3} a^{2} + \frac{40}{3} a\) , \( \frac{41}{3} a^{3} - \frac{86}{3} a^{2} - \frac{194}{3} a + 110\bigr] \)
|
| 45.3-e3
| \( \bigl[a + 1\) , \( -\frac{1}{3} a^{3} + \frac{4}{3} a^{2} + \frac{1}{3} a - 4\) , \( 1\) , \( \frac{10}{3} a^{3} - \frac{28}{3} a^{2} - \frac{10}{3} a + 13\) , \( \frac{44}{3} a^{3} - \frac{134}{3} a^{2} - \frac{29}{3} a + 63\bigr] \)
|
| 45.3-e4
| \( \bigl[a + 1\) , \( -\frac{1}{3} a^{3} + \frac{4}{3} a^{2} + \frac{1}{3} a - 4\) , \( 1\) , \( 5 a^{3} - 16 a^{2} - 5 a + 23\) , \( \frac{16}{3} a^{3} - \frac{49}{3} a^{2} - \frac{7}{3} a + 22\bigr] \)
|
Rank: \( 1 \)
\(\left(\begin{array}{rrrr}
1 & 2 & 3 & 6 \\
2 & 1 & 6 & 3 \\
3 & 6 & 1 & 2 \\
6 & 3 & 2 & 1
\end{array}\right)\)
