Elliptic curves in class 11.1-b over 4.4.18625.1
Isogeny class 11.1-b contains
4 curves linked by isogenies of
degrees dividing 4.
| Curve label |
Weierstrass Coefficients |
| 11.1-b1
| \( \bigl[a^{2} - 6\) , \( -\frac{1}{6} a^{3} + a^{2} + \frac{1}{3} a - \frac{37}{6}\) , \( \frac{1}{6} a^{3} + a^{2} - \frac{4}{3} a - \frac{35}{6}\) , \( 228 a^{3} + 349 a^{2} - 2374 a - 3918\) , \( \frac{8573}{3} a^{3} + 4234 a^{2} - \frac{88993}{3} a - \frac{143503}{3}\bigr] \)
|
| 11.1-b2
| \( \bigl[\frac{1}{6} a^{3} + a^{2} - \frac{1}{3} a - \frac{35}{6}\) , \( -a - 1\) , \( a^{2} + a - 6\) , \( \frac{107}{6} a^{3} + 34 a^{2} - \frac{524}{3} a - \frac{2023}{6}\) , \( -\frac{337}{3} a^{3} - 142 a^{2} + \frac{3587}{3} a + \frac{5222}{3}\bigr] \)
|
| 11.1-b3
| \( \bigl[a\) , \( -\frac{1}{6} a^{3} + a^{2} + \frac{4}{3} a - \frac{49}{6}\) , \( \frac{1}{6} a^{3} + a^{2} - \frac{4}{3} a - \frac{35}{6}\) , \( \frac{1}{2} a^{3} - 5 a + \frac{11}{2}\) , \( -\frac{1}{6} a^{3} + a^{2} + \frac{7}{3} a - \frac{55}{6}\bigr] \)
|
| 11.1-b4
| \( \bigl[a\) , \( \frac{1}{6} a^{3} - \frac{1}{3} a + \frac{1}{6}\) , \( \frac{1}{6} a^{3} - \frac{4}{3} a + \frac{7}{6}\) , \( -2 a^{3} + 8 a^{2} + 19 a - 63\) , \( -\frac{22}{3} a^{3} + 22 a^{2} + \frac{218}{3} a - \frac{607}{3}\bigr] \)
|
Rank: \( 1 \)
\(\left(\begin{array}{rrrr}
1 & 2 & 4 & 4 \\
2 & 1 & 2 & 2 \\
4 & 2 & 1 & 4 \\
4 & 2 & 4 & 1
\end{array}\right)\)
