Elliptic curves in class 19.1-a over 4.4.10025.1
Isogeny class 19.1-a contains
4 curves linked by isogenies of
degrees dividing 4.
| Curve label |
Weierstrass Coefficients |
| 19.1-a1
| \( \bigl[\frac{1}{2} a^{3} + \frac{3}{2} a^{2} - \frac{5}{2} a - 8\) , \( 0\) , \( a + 1\) , \( 5 a^{3} - 10 a^{2} - 10 a + 10\) , \( \frac{37}{2} a^{3} - \frac{125}{2} a^{2} + \frac{7}{2} a + 93\bigr] \)
|
| 19.1-a2
| \( \bigl[\frac{1}{2} a^{3} + \frac{3}{2} a^{2} - \frac{5}{2} a - 7\) , \( -a^{2} + 5\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - 2\) , \( -\frac{19}{2} a^{3} - \frac{37}{2} a^{2} + \frac{113}{2} a + 84\) , \( -84 a^{3} - 143 a^{2} + 547 a + 640\bigr] \)
|
| 19.1-a3
| \( \bigl[a + 1\) , \( 0\) , \( a^{3} + 2 a^{2} - 7 a - 11\) , \( -148 a^{3} - 247 a^{2} + 969 a + 1109\) , \( -\frac{187}{2} a^{3} - \frac{323}{2} a^{2} + \frac{1179}{2} a + 681\bigr] \)
|
| 19.1-a4
| \( \bigl[a + 1\) , \( -a^{3} - 2 a^{2} + 7 a + 11\) , \( a + 1\) , \( -7 a^{3} + 11 a^{2} + 38 a - 54\) , \( \frac{273}{2} a^{3} - \frac{1159}{2} a^{2} + \frac{573}{2} a + 766\bigr] \)
|
Rank: \( 1 \)
\(\left(\begin{array}{rrrr}
1 & 2 & 4 & 4 \\
2 & 1 & 2 & 2 \\
4 & 2 & 1 & 4 \\
4 & 2 & 4 & 1
\end{array}\right)\)
