Elliptic curves in class 47.4-b over 4.4.4913.1
Isogeny class 47.4-b contains
4 curves linked by isogenies of
degrees dividing 4.
| Curve label |
Weierstrass Coefficients |
| 47.4-b1
| \( \bigl[\frac{1}{2} a^{3} - 2 a - \frac{3}{2}\) , \( -a\) , \( a^{2} - 3\) , \( -8 a^{3} - 20 a^{2} - 5 a + 5\) , \( 42 a^{3} + 82 a^{2} - 17 a - 18\bigr] \)
|
| 47.4-b2
| \( \bigl[a\) , \( \frac{1}{2} a^{3} - 3 a - \frac{1}{2}\) , \( a\) , \( -41 a^{3} - 78 a^{2} + 39 a + 5\) , \( \frac{1409}{2} a^{3} + 1352 a^{2} - 353 a - \frac{463}{2}\bigr] \)
|
| 47.4-b3
| \( \bigl[1\) , \( -a^{3} + a^{2} + 6 a - 1\) , \( -\frac{1}{2} a^{3} + a^{2} + 2 a - \frac{3}{2}\) , \( 5 a^{3} - 12 a^{2} - 7 a - 2\) , \( -13 a^{3} + 37 a^{2} + 4 a - 5\bigr] \)
|
| 47.4-b4
| \( \bigl[1\) , \( -\frac{1}{2} a^{3} + a^{2} + 3 a - \frac{1}{2}\) , \( a^{2} - a - 3\) , \( -32 a^{3} + 41 a^{2} + 176 a - 90\) , \( -\frac{119}{2} a^{3} + 81 a^{2} + 331 a - \frac{353}{2}\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrr}
1 & 4 & 4 & 2 \\
4 & 1 & 4 & 2 \\
4 & 4 & 1 & 2 \\
2 & 2 & 2 & 1
\end{array}\right)\)
