Elliptic curves in class 19.1-a over 4.4.2225.1
Isogeny class 19.1-a contains
6 curves linked by isogenies of
degrees dividing 8.
| Curve label |
Weierstrass Coefficients |
| 19.1-a1
| \( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{3}{2} a - 3\) , \( -\frac{1}{2} a^{3} + \frac{3}{2} a^{2} + \frac{3}{2} a - 2\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - 3\) , \( -3 a^{3} - 3 a^{2} + 5 a + 4\) , \( -16 a^{3} - 23 a^{2} + 25 a + 27\bigr] \)
|
| 19.1-a2
| \( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{3}{2} a\) , \( -a^{2} + a + 3\) , \( a^{2} - 2\) , \( 6 a^{3} - 28 a^{2} + 35 a - 9\) , \( -\frac{139}{2} a^{3} + \frac{313}{2} a^{2} + \frac{267}{2} a - 251\bigr] \)
|
| 19.1-a3
| \( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{3}{2} a\) , \( -a^{2} + a + 3\) , \( a^{2} - 2\) , \( \frac{17}{2} a^{3} - \frac{51}{2} a^{2} + \frac{5}{2} a + 21\) , \( \frac{67}{2} a^{3} - \frac{189}{2} a^{2} - \frac{3}{2} a + 76\bigr] \)
|
| 19.1-a4
| \( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{3}{2} a\) , \( -\frac{1}{2} a^{3} - \frac{1}{2} a^{2} + \frac{7}{2} a + 4\) , \( a + 1\) , \( -a^{3} - a^{2} + 6 a + 5\) , \( \frac{3}{2} a^{3} - \frac{1}{2} a^{2} - \frac{15}{2} a - 5\bigr] \)
|
| 19.1-a5
| \( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{3}{2} a + 1\) , \( a^{2} - 2 a - 2\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{3}{2} a\) , \( 2 a^{2} - 2 a - 3\) , \( \frac{1}{2} a^{3} + \frac{3}{2} a^{2} - \frac{3}{2} a - 2\bigr] \)
|
| 19.1-a6
| \( \bigl[1\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{1}{2} a\) , \( a\) , \( 4 a^{3} + a^{2} - 14 a - 8\) , \( -5 a^{3} - 7 a^{2} + 17 a + 23\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrrrr}
1 & 8 & 4 & 2 & 8 & 4 \\
8 & 1 & 2 & 4 & 4 & 8 \\
4 & 2 & 1 & 2 & 2 & 4 \\
2 & 4 & 2 & 1 & 4 & 2 \\
8 & 4 & 2 & 4 & 1 & 8 \\
4 & 8 & 4 & 2 & 8 & 1
\end{array}\right)\)
