Rank: \( 0 \)
\(\left(\begin{array}{rrrr}
1 & 2 & 4 & 4 \\
2 & 1 & 2 & 2 \\
4 & 2 & 1 & 4 \\
4 & 2 & 4 & 1
\end{array}\right)\)
Elliptic curves in class 16.2-b over 4.4.13968.1
Isogeny class 16.2-b contains
4 curves linked by isogenies of
degrees dividing 4.
| Curve label |
Weierstrass Coefficients |
| 16.2-b1
| \( \bigl[\frac{1}{2} a^{3} - \frac{5}{2} a - 1\) , \( -\frac{1}{2} a^{2} - \frac{1}{2} a + 3\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 2 a + 2\) , \( a^{3} + \frac{1}{2} a^{2} - \frac{7}{2} a + 1\) , \( \frac{5}{2} a^{3} + \frac{5}{2} a^{2} - 9 a - 5\bigr] \)
|
| 16.2-b2
| \( \bigl[\frac{1}{2} a^{3} - \frac{5}{2} a - 1\) , \( -\frac{1}{2} a^{2} + \frac{1}{2} a + 3\) , \( \frac{1}{2} a^{3} - \frac{7}{2} a - 1\) , \( -\frac{1}{2} a^{3} + \frac{21}{2} a^{2} + 7 a - 44\) , \( \frac{25}{2} a^{3} - 5 a^{2} - \frac{139}{2} a + 15\bigr] \)
|
| 16.2-b3
| \( \bigl[\frac{1}{2} a^{2} + \frac{1}{2} a - 1\) , \( -\frac{1}{2} a^{2} + \frac{1}{2} a + 2\) , \( \frac{1}{2} a^{3} - \frac{5}{2} a - 1\) , \( a^{3} - \frac{17}{2} a^{2} + \frac{15}{2} a + 4\) , \( -\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - a - 2\bigr] \)
|
| 16.2-b4
| \( \bigl[a\) , \( -\frac{1}{2} a^{2} + \frac{1}{2} a + 2\) , \( a\) , \( 33 a^{3} - 21 a^{2} - 259 a - 94\) , \( 389 a^{3} - 239 a^{2} - 3054 a - 1122\bigr] \)
|
