Elliptic curves in class 45.3-d over 4.4.4525.1
Isogeny class 45.3-d contains
4 curves linked by isogenies of
degrees dividing 10.
| Curve label |
Weierstrass Coefficients |
| 45.3-d1
| \( \bigl[a^{2} - 3\) , \( \frac{1}{3} a^{3} + \frac{2}{3} a^{2} - \frac{10}{3} a - 5\) , \( \frac{1}{3} a^{3} + \frac{2}{3} a^{2} - \frac{4}{3} a - 4\) , \( -\frac{22}{3} a^{3} - \frac{50}{3} a^{2} + \frac{76}{3} a + 36\) , \( 27 a^{3} + 54 a^{2} - 71 a - 109\bigr] \)
|
| 45.3-d2
| \( \bigl[a^{2} - 3\) , \( \frac{1}{3} a^{3} - \frac{4}{3} a^{2} - \frac{4}{3} a + 3\) , \( \frac{1}{3} a^{3} + \frac{2}{3} a^{2} - \frac{7}{3} a - 3\) , \( \frac{295}{3} a^{3} + \frac{131}{3} a^{2} - \frac{1894}{3} a - 623\) , \( -\frac{3827}{3} a^{3} - \frac{1723}{3} a^{2} + \frac{24299}{3} a + 7921\bigr] \)
|
| 45.3-d3
| \( \bigl[a^{2} - 3\) , \( \frac{1}{3} a^{3} - \frac{4}{3} a^{2} - \frac{4}{3} a + 3\) , \( \frac{1}{3} a^{3} + \frac{2}{3} a^{2} - \frac{7}{3} a - 3\) , \( -\frac{10}{3} a^{3} + \frac{1}{3} a^{2} + \frac{61}{3} a + 12\) , \( -\frac{214}{3} a^{3} - \frac{98}{3} a^{2} + \frac{1363}{3} a + 447\bigr] \)
|
| 45.3-d4
| \( \bigl[a\) , \( \frac{1}{3} a^{3} - \frac{1}{3} a^{2} - \frac{1}{3} a\) , \( a^{2} - a - 3\) , \( \frac{19}{3} a^{3} - \frac{238}{3} a^{2} - \frac{7}{3} a + 101\) , \( \frac{361}{3} a^{3} + \frac{341}{3} a^{2} - \frac{916}{3} a - 314\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrr}
1 & 10 & 5 & 2 \\
10 & 1 & 2 & 5 \\
5 & 2 & 1 & 10 \\
2 & 5 & 10 & 1
\end{array}\right)\)
