Elliptic curves in class 16.3-a over 4.4.4913.1
Isogeny class 16.3-a contains
4 curves linked by isogenies of
degrees dividing 4.
| Curve label |
Weierstrass Coefficients |
| 16.3-a1
| \( \bigl[a^{2} - 3\) , \( a^{3} - a^{2} - 5 a + 1\) , \( 0\) , \( a^{3} + a^{2} - a + 3\) , \( a^{3} + 2 a^{2} - a - 2\bigr] \)
|
| 16.3-a2
| \( \bigl[a^{2} - a - 2\) , \( -a^{3} + a^{2} + 5 a - 1\) , \( a + 1\) , \( \frac{83}{2} a^{3} - 20 a^{2} - 265 a - \frac{177}{2}\) , \( 291 a^{3} - 149 a^{2} - 1820 a - 593\bigr] \)
|
| 16.3-a3
| \( \bigl[a^{2} - a - 2\) , \( -a^{3} + a^{2} + 5 a - 1\) , \( a + 1\) , \( 14 a^{3} - 10 a^{2} - 100 a - 31\) , \( -37 a^{3} + 28 a^{2} + 253 a + 82\bigr] \)
|
| 16.3-a4
| \( \bigl[a^{2} - a - 2\) , \( -a^{3} + a^{2} + 5 a - 1\) , \( a + 1\) , \( \frac{3}{2} a^{3} - 15 a - \frac{7}{2}\) , \( \frac{11}{2} a^{3} - 2 a^{2} - 37 a - \frac{25}{2}\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrr}
1 & 4 & 4 & 2 \\
4 & 1 & 4 & 2 \\
4 & 4 & 1 & 2 \\
2 & 2 & 2 & 1
\end{array}\right)\)
