Elliptic curves in class 25.1-c over 4.4.9225.1
Isogeny class 25.1-c contains
6 curves linked by isogenies of
degrees dividing 8.
| Curve label |
Weierstrass Coefficients |
| 25.1-c1
| \( \bigl[\frac{1}{4} a^{3} + a^{2} - \frac{3}{2} a - \frac{19}{4}\) , \( -\frac{1}{4} a^{3} + \frac{1}{2} a - \frac{5}{4}\) , \( \frac{1}{4} a^{3} + a^{2} - \frac{3}{2} a - \frac{19}{4}\) , \( 300 a^{3} - 661 a^{2} - 2203 a + 4733\) , \( 16056 a^{3} - 35321 a^{2} - 118221 a + 254320\bigr] \)
|
| 25.1-c2
| \( \bigl[\frac{1}{4} a^{3} + a^{2} - \frac{3}{2} a - \frac{19}{4}\) , \( -\frac{1}{4} a^{3} - a^{2} + \frac{5}{2} a + \frac{15}{4}\) , \( \frac{1}{4} a^{3} - \frac{3}{2} a + \frac{1}{4}\) , \( -\frac{687}{4} a^{3} - 292 a^{2} + \frac{1835}{2} a + \frac{4905}{4}\) , \( \frac{9607}{4} a^{3} + 4492 a^{2} - \frac{22469}{2} a - \frac{63205}{4}\bigr] \)
|
| 25.1-c3
| \( \bigl[a^{2} - 4\) , \( a^{2} - a - 4\) , \( a^{2} - 4\) , \( \frac{9}{4} a^{3} - 12 a^{2} + \frac{9}{2} a + \frac{93}{4}\) , \( \frac{31}{4} a^{3} - 30 a^{2} + \frac{3}{2} a + \frac{227}{4}\bigr] \)
|
| 25.1-c4
| \( \bigl[a^{2} - 4\) , \( a^{2} - a - 4\) , \( a^{2} - 4\) , \( 31 a^{3} - 167 a^{2} + 47 a + 347\) , \( -\frac{1957}{4} a^{3} + 1971 a^{2} - \frac{269}{2} a - \frac{15389}{4}\bigr] \)
|
| 25.1-c5
| \( \bigl[a^{2} - 4\) , \( -\frac{1}{4} a^{3} + \frac{3}{2} a + \frac{3}{4}\) , \( \frac{1}{4} a^{3} + a^{2} - \frac{3}{2} a - \frac{15}{4}\) , \( -a^{3} + 6 a - 2\) , \( -\frac{1}{4} a^{3} + a^{2} + \frac{1}{2} a - \frac{41}{4}\bigr] \)
|
| 25.1-c6
| \( \bigl[1\) , \( \frac{1}{4} a^{3} - \frac{3}{2} a + \frac{1}{4}\) , \( \frac{1}{4} a^{3} + a^{2} - \frac{1}{2} a - \frac{19}{4}\) , \( \frac{1}{4} a^{3} - a^{2} - \frac{5}{2} a + \frac{25}{4}\) , \( -\frac{3}{2} a^{3} + 9 a - \frac{11}{2}\bigr] \)
|
Rank: \( 1 \)
\(\left(\begin{array}{rrrrrr}
1 & 4 & 4 & 2 & 8 & 8 \\
4 & 1 & 4 & 2 & 8 & 8 \\
4 & 4 & 1 & 2 & 2 & 2 \\
2 & 2 & 2 & 1 & 4 & 4 \\
8 & 8 & 2 & 4 & 1 & 4 \\
8 & 8 & 2 & 4 & 4 & 1
\end{array}\right)\)
