Elliptic curves in class 25.1-d over 4.4.9225.1
Isogeny class 25.1-d contains
6 curves linked by isogenies of
degrees dividing 8.
| Curve label |
Weierstrass Coefficients |
| 25.1-d1
| \( \bigl[a\) , \( -\frac{1}{4} a^{3} - a^{2} + \frac{3}{2} a + \frac{23}{4}\) , \( \frac{1}{4} a^{3} - \frac{1}{2} a + \frac{1}{4}\) , \( -\frac{3}{2} a^{3} - 4 a^{2} + 8 a + \frac{33}{2}\) , \( -\frac{23}{4} a^{3} - 11 a^{2} + \frac{57}{2} a + \frac{165}{4}\bigr] \)
|
| 25.1-d2
| \( \bigl[\frac{1}{4} a^{3} - \frac{3}{2} a + \frac{1}{4}\) , \( \frac{1}{4} a^{3} - \frac{1}{2} a - \frac{3}{4}\) , \( \frac{1}{4} a^{3} + a^{2} - \frac{3}{2} a - \frac{19}{4}\) , \( -\frac{3}{4} a^{3} - 3 a^{2} + \frac{53}{2} a - \frac{143}{4}\) , \( -2 a^{3} - 11 a^{2} + 77 a - 95\bigr] \)
|
| 25.1-d3
| \( \bigl[\frac{1}{4} a^{3} - \frac{3}{2} a + \frac{1}{4}\) , \( \frac{1}{4} a^{3} - \frac{1}{2} a - \frac{3}{4}\) , \( \frac{1}{4} a^{3} + a^{2} - \frac{3}{2} a - \frac{19}{4}\) , \( -\frac{3}{4} a^{3} + 2 a^{2} + \frac{13}{2} a - \frac{63}{4}\) , \( \frac{5}{4} a^{3} - 3 a^{2} - \frac{23}{2} a + \frac{101}{4}\bigr] \)
|
| 25.1-d4
| \( \bigl[\frac{1}{4} a^{3} - \frac{1}{2} a + \frac{1}{4}\) , \( -\frac{1}{4} a^{3} + a^{2} + \frac{1}{2} a - \frac{17}{4}\) , \( a^{2} - 4\) , \( -\frac{5}{2} a^{3} + 7 a + \frac{15}{2}\) , \( -\frac{17}{4} a^{3} - 2 a^{2} + \frac{33}{2} a + \frac{51}{4}\bigr] \)
|
| 25.1-d5
| \( \bigl[\frac{1}{4} a^{3} - \frac{1}{2} a + \frac{1}{4}\) , \( \frac{1}{4} a^{3} + a^{2} - \frac{3}{2} a - \frac{15}{4}\) , \( \frac{1}{4} a^{3} + a^{2} - \frac{3}{2} a - \frac{15}{4}\) , \( -\frac{241}{4} a^{3} - 53 a^{2} + \frac{915}{2} a + \frac{1799}{4}\) , \( \frac{707}{2} a^{3} + 404 a^{2} - 2799 a - \frac{7087}{2}\bigr] \)
|
| 25.1-d6
| \( \bigl[1\) , \( \frac{1}{4} a^{3} - a^{2} - \frac{5}{2} a + \frac{21}{4}\) , \( \frac{1}{4} a^{3} + a^{2} - \frac{1}{2} a - \frac{15}{4}\) , \( 15 a^{3} - 53 a^{2} - 15 a + 120\) , \( \frac{809}{2} a^{3} - 1502 a^{2} + a + \frac{5709}{2}\bigr] \)
|
Rank: \( 1 \)
\(\left(\begin{array}{rrrrrr}
1 & 4 & 2 & 4 & 8 & 8 \\
4 & 1 & 2 & 4 & 2 & 2 \\
2 & 2 & 1 & 2 & 4 & 4 \\
4 & 4 & 2 & 1 & 8 & 8 \\
8 & 2 & 4 & 8 & 1 & 4 \\
8 & 2 & 4 & 8 & 4 & 1
\end{array}\right)\)
