Elliptic curves in class 11.2-b over 4.4.18625.1
Isogeny class 11.2-b contains
4 curves linked by isogenies of
degrees dividing 4.
| Curve label |
Weierstrass Coefficients |
| 11.2-b1
| \( \bigl[\frac{1}{6} a^{3} + a^{2} - \frac{4}{3} a - \frac{41}{6}\) , \( -\frac{1}{6} a^{3} + a^{2} + \frac{7}{3} a - \frac{43}{6}\) , \( a\) , \( \frac{491}{6} a^{3} - 344 a^{2} - \frac{320}{3} a + \frac{6797}{6}\) , \( \frac{2171}{2} a^{3} - 4563 a^{2} - 1401 a + \frac{29867}{2}\bigr] \)
|
| 11.2-b2
| \( \bigl[\frac{1}{6} a^{3} + a^{2} - \frac{1}{3} a - \frac{41}{6}\) , \( -\frac{1}{6} a^{3} + \frac{1}{3} a + \frac{5}{6}\) , \( 1\) , \( \frac{22}{3} a^{3} - 21 a^{2} - \frac{62}{3} a + \frac{205}{3}\) , \( -\frac{193}{6} a^{3} + 102 a^{2} + \frac{202}{3} a - \frac{1825}{6}\bigr] \)
|
| 11.2-b3
| \( \bigl[\frac{1}{6} a^{3} - \frac{1}{3} a + \frac{1}{6}\) , \( a^{2} - 7\) , \( a^{2} - 6\) , \( \frac{4}{3} a^{3} + 2 a^{2} - \frac{41}{3} a - \frac{11}{3}\) , \( -\frac{1}{6} a^{3} + 5 a^{2} + \frac{13}{3} a - \frac{205}{6}\bigr] \)
|
| 11.2-b4
| \( \bigl[\frac{1}{6} a^{3} - \frac{1}{3} a + \frac{1}{6}\) , \( \frac{1}{6} a^{3} - a^{2} - \frac{7}{3} a + \frac{43}{6}\) , \( \frac{1}{6} a^{3} - \frac{4}{3} a + \frac{7}{6}\) , \( -3 a^{3} - 9 a^{2} + 20 a + 63\) , \( -\frac{26}{3} a^{3} - 22 a^{2} + \frac{166}{3} a + \frac{379}{3}\bigr] \)
|
Rank: \( 1 \)
\(\left(\begin{array}{rrrr}
1 & 2 & 4 & 4 \\
2 & 1 & 2 & 2 \\
4 & 2 & 1 & 4 \\
4 & 2 & 4 & 1
\end{array}\right)\)
