Elliptic curves in class 45.3-c over 4.4.4525.1
Isogeny class 45.3-c contains
4 curves linked by isogenies of
degrees dividing 6.
| Curve label |
Weierstrass Coefficients |
| 45.3-c1
| \( \bigl[\frac{1}{3} a^{3} + \frac{2}{3} a^{2} - \frac{7}{3} a - 4\) , \( \frac{1}{3} a^{3} - \frac{1}{3} a^{2} - \frac{1}{3} a - 1\) , \( \frac{1}{3} a^{3} - \frac{1}{3} a^{2} - \frac{4}{3} a + 1\) , \( \frac{7}{3} a^{3} - \frac{22}{3} a^{2} + \frac{2}{3} a + 14\) , \( -6 a^{3} + 18 a^{2} + 6 a - 24\bigr] \)
|
| 45.3-c2
| \( \bigl[\frac{1}{3} a^{3} + \frac{2}{3} a^{2} - \frac{7}{3} a - 4\) , \( \frac{1}{3} a^{3} - \frac{1}{3} a^{2} - \frac{1}{3} a - 1\) , \( \frac{1}{3} a^{3} - \frac{1}{3} a^{2} - \frac{4}{3} a + 1\) , \( \frac{77}{3} a^{3} - \frac{257}{3} a^{2} - \frac{38}{3} a + 124\) , \( \frac{544}{3} a^{3} - \frac{1693}{3} a^{2} - \frac{349}{3} a + 800\bigr] \)
|
| 45.3-c3
| \( \bigl[\frac{1}{3} a^{3} + \frac{2}{3} a^{2} - \frac{7}{3} a - 3\) , \( -\frac{1}{3} a^{3} + \frac{1}{3} a^{2} + \frac{1}{3} a - 1\) , \( \frac{1}{3} a^{3} - \frac{1}{3} a^{2} - \frac{1}{3} a\) , \( -\frac{37}{3} a^{3} - \frac{641}{3} a^{2} + \frac{274}{3} a + 344\) , \( -1000 a^{3} - 113 a^{2} + 1747 a + 723\bigr] \)
|
| 45.3-c4
| \( \bigl[a^{2} - 3\) , \( -\frac{1}{3} a^{3} - \frac{2}{3} a^{2} + \frac{7}{3} a + 5\) , \( \frac{1}{3} a^{3} + \frac{2}{3} a^{2} - \frac{7}{3} a - 4\) , \( -\frac{1}{3} a^{3} - \frac{2}{3} a^{2} - \frac{8}{3} a - 6\) , \( 3 a^{3} - 4 a^{2} - 37 a - 33\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrr}
1 & 2 & 6 & 3 \\
2 & 1 & 3 & 6 \\
6 & 3 & 1 & 2 \\
3 & 6 & 2 & 1
\end{array}\right)\)
