Elliptic curves in class 19.2-a over 4.4.10025.1
Isogeny class 19.2-a contains
4 curves linked by isogenies of
degrees dividing 4.
| Curve label |
Weierstrass Coefficients |
| 19.2-a1
| \( \bigl[\frac{1}{2} a^{3} + \frac{3}{2} a^{2} - \frac{5}{2} a - 8\) , \( -\frac{1}{2} a^{3} - \frac{1}{2} a^{2} + \frac{5}{2} a + 4\) , \( a^{3} + 2 a^{2} - 6 a - 11\) , \( -2 a^{3} - 9 a^{2} + 55 a - 53\) , \( 24 a^{3} - 119 a^{2} + 124 a + 56\bigr] \)
|
| 19.2-a2
| \( \bigl[\frac{1}{2} a^{3} + \frac{3}{2} a^{2} - \frac{5}{2} a - 8\) , \( -\frac{1}{2} a^{3} - \frac{1}{2} a^{2} + \frac{5}{2} a + 4\) , \( a^{3} + 2 a^{2} - 6 a - 11\) , \( -\frac{9}{2} a^{3} + \frac{7}{2} a^{2} + \frac{75}{2} a - 48\) , \( -18 a^{3} + 32 a^{2} + 166 a - 334\bigr] \)
|
| 19.2-a3
| \( \bigl[\frac{1}{2} a^{3} + \frac{3}{2} a^{2} - \frac{5}{2} a - 7\) , \( -\frac{1}{2} a^{3} - \frac{3}{2} a^{2} + \frac{5}{2} a + 8\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - 3\) , \( \frac{77}{2} a^{3} + \frac{103}{2} a^{2} - \frac{593}{2} a - 305\) , \( 206 a^{3} + 286 a^{2} - 1575 a - 1704\bigr] \)
|
| 19.2-a4
| \( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - 3\) , \( 0\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - 3\) , \( -\frac{81}{2} a^{3} - \frac{121}{2} a^{2} + \frac{589}{2} a + 326\) , \( 1831 a^{3} + 2546 a^{2} - 14059 a - 15314\bigr] \)
|
Rank: \( 1 \)
\(\left(\begin{array}{rrrr}
1 & 2 & 4 & 4 \\
2 & 1 & 2 & 2 \\
4 & 2 & 1 & 4 \\
4 & 2 & 4 & 1
\end{array}\right)\)
