Elliptic curves in class 19.2-a over 4.4.2225.1
Isogeny class 19.2-a contains
6 curves linked by isogenies of
degrees dividing 8.
| Curve label |
Weierstrass Coefficients |
| 19.2-a1
| \( \bigl[a^{2} - 3\) , \( -a^{2} + 2 a + 2\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - 3\) , \( -\frac{21}{2} a^{3} + \frac{41}{2} a^{2} + \frac{67}{2} a - 50\) , \( -\frac{59}{2} a^{3} + \frac{109}{2} a^{2} + \frac{211}{2} a - 153\bigr] \)
|
| 19.2-a2
| \( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{3}{2} a\) , \( a^{2} - 2 a - 3\) , \( a\) , \( -a^{2} + 2 a + 1\) , \( a^{3} - 3 a^{2} + 2\bigr] \)
|
| 19.2-a3
| \( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{3}{2} a\) , \( a^{2} - a - 2\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{3}{2} a - 2\) , \( 22 a^{3} - 120 a - 88\) , \( -63 a^{3} - 25 a^{2} + 263 a + 199\bigr] \)
|
| 19.2-a4
| \( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{3}{2} a + 1\) , \( -\frac{1}{2} a^{3} - \frac{1}{2} a^{2} + \frac{7}{2} a + 2\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{3}{2} a\) , \( -2 a^{2} + 2 a + 7\) , \( \frac{3}{2} a^{3} - \frac{7}{2} a^{2} - \frac{9}{2} a + 10\bigr] \)
|
| 19.2-a5
| \( \bigl[1\) , \( a^{2} - 2\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{3}{2} a - 2\) , \( \frac{1}{2} a^{3} - \frac{3}{2} a^{2} - \frac{15}{2} a - 5\) , \( -\frac{3}{2} a^{3} - \frac{13}{2} a^{2} - \frac{17}{2} a - 3\bigr] \)
|
| 19.2-a6
| \( \bigl[1\) , \( -\frac{1}{2} a^{3} + \frac{1}{2} a^{2} + \frac{1}{2} a + 1\) , \( a + 1\) , \( 5 a^{3} - 8 a^{2} - 16 a + 15\) , \( -9 a^{3} + 20 a^{2} + 29 a - 56\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrrrr}
1 & 2 & 8 & 8 & 4 & 4 \\
2 & 1 & 4 & 4 & 2 & 2 \\
8 & 4 & 1 & 4 & 2 & 8 \\
8 & 4 & 4 & 1 & 2 & 8 \\
4 & 2 & 2 & 2 & 1 & 4 \\
4 & 2 & 8 & 8 & 4 & 1
\end{array}\right)\)
