Elliptic curves in class 47.1-b over 4.4.4913.1
Isogeny class 47.1-b contains
4 curves linked by isogenies of
degrees dividing 4.
| Curve label |
Weierstrass Coefficients |
| 47.1-b1
| \( \bigl[\frac{1}{2} a^{3} - 3 a - \frac{3}{2}\) , \( -a^{3} + a^{2} + 6 a\) , \( \frac{1}{2} a^{3} - 3 a - \frac{3}{2}\) , \( \frac{605}{2} a^{3} - 160 a^{2} - 1893 a - \frac{1239}{2}\) , \( -5374 a^{3} + 2761 a^{2} + 33596 a + 11016\bigr] \)
|
| 47.1-b2
| \( \bigl[-\frac{1}{2} a^{3} + a^{2} + 3 a - \frac{1}{2}\) , \( -\frac{1}{2} a^{3} + 3 a + \frac{3}{2}\) , \( -\frac{1}{2} a^{3} + a^{2} + 2 a - \frac{1}{2}\) , \( \frac{141}{2} a^{3} - 36 a^{2} - 442 a - \frac{291}{2}\) , \( -\frac{651}{2} a^{3} + 166 a^{2} + 2036 a + \frac{1335}{2}\bigr] \)
|
| 47.1-b3
| \( \bigl[1\) , \( \frac{1}{2} a^{3} - a^{2} - 2 a + \frac{3}{2}\) , \( a\) , \( -\frac{7}{2} a^{3} - 2 a^{2} + 9 a - \frac{9}{2}\) , \( \frac{15}{2} a^{3} + 11 a^{2} - 8 a + \frac{1}{2}\bigr] \)
|
| 47.1-b4
| \( \bigl[1\) , \( -\frac{1}{2} a^{3} + 4 a + \frac{5}{2}\) , \( a^{2} - a - 2\) , \( 10 a^{3} - 23 a^{2} - 18 a - 2\) , \( 11 a^{3} - 39 a^{2} + 16 a + 10\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrr}
1 & 4 & 4 & 2 \\
4 & 1 & 4 & 2 \\
4 & 4 & 1 & 2 \\
2 & 2 & 2 & 1
\end{array}\right)\)
