Elliptic curves in class 5.1-a over 4.4.13025.1
Isogeny class 5.1-a contains
6 curves linked by isogenies of
degrees dividing 8.
| Curve label |
Weierstrass Coefficients |
| 5.1-a1
| \( \bigl[-\frac{1}{4} a^{3} + \frac{3}{2} a^{2} + \frac{1}{2} a - \frac{25}{4}\) , \( -\frac{1}{4} a^{3} + \frac{3}{2} a^{2} + \frac{1}{2} a - \frac{29}{4}\) , \( a^{2} - a - 5\) , \( -\frac{2735}{4} a^{3} + \frac{3951}{2} a^{2} + \frac{8953}{2} a - \frac{42055}{4}\) , \( -\frac{89057}{4} a^{3} + \frac{128577}{2} a^{2} + \frac{291655}{2} a - \frac{1368261}{4}\bigr] \)
|
| 5.1-a2
| \( \bigl[-\frac{1}{4} a^{3} + \frac{3}{2} a^{2} + \frac{1}{2} a - \frac{25}{4}\) , \( -\frac{1}{4} a^{3} + \frac{3}{2} a^{2} + \frac{1}{2} a - \frac{29}{4}\) , \( a^{2} - a - 5\) , \( -\frac{15}{2} a^{3} + 23 a^{2} + 44 a - \frac{225}{2}\) , \( \frac{43}{4} a^{3} - \frac{59}{2} a^{2} - \frac{153}{2} a + \frac{671}{4}\bigr] \)
|
| 5.1-a3
| \( \bigl[1\) , \( \frac{1}{4} a^{3} - \frac{3}{2} a^{2} - \frac{3}{2} a + \frac{25}{4}\) , \( \frac{1}{4} a^{3} - \frac{1}{2} a^{2} - \frac{1}{2} a + \frac{5}{4}\) , \( \frac{61}{2} a^{3} - 103 a^{2} - 113 a + \frac{721}{2}\) , \( -\frac{1013}{4} a^{3} + \frac{1731}{2} a^{2} + \frac{1871}{2} a - \frac{12089}{4}\bigr] \)
|
| 5.1-a4
| \( \bigl[\frac{1}{4} a^{3} - \frac{1}{2} a^{2} - \frac{3}{2} a + \frac{9}{4}\) , \( -a - 1\) , \( a^{2} - 5\) , \( -\frac{7}{2} a^{3} + a^{2} + 12 a - \frac{5}{2}\) , \( \frac{39}{4} a^{3} + \frac{27}{2} a^{2} - \frac{65}{2} a - \frac{177}{4}\bigr] \)
|
| 5.1-a5
| \( \bigl[\frac{1}{4} a^{3} - \frac{1}{2} a^{2} - \frac{3}{2} a + \frac{9}{4}\) , \( -\frac{1}{4} a^{3} + \frac{1}{2} a^{2} + \frac{1}{2} a - \frac{1}{4}\) , \( a^{2} - 5\) , \( -4 a^{2} - 25 a - 29\) , \( -\frac{1}{4} a^{3} - \frac{41}{2} a^{2} - \frac{179}{2} a - \frac{389}{4}\bigr] \)
|
| 5.1-a6
| \( \bigl[\frac{1}{4} a^{3} - \frac{1}{2} a^{2} - \frac{3}{2} a + \frac{9}{4}\) , \( -\frac{1}{4} a^{3} + \frac{1}{2} a^{2} + \frac{1}{2} a - \frac{1}{4}\) , \( a^{2} - 5\) , \( -\frac{15}{4} a^{3} - \frac{23}{2} a^{2} + \frac{45}{2} a + \frac{249}{4}\) , \( 32 a^{3} - 11 a^{2} - 411 a - 521\bigr] \)
|
Rank: \( 1 \)
\(\left(\begin{array}{rrrrrr}
1 & 4 & 8 & 8 & 2 & 4 \\
4 & 1 & 2 & 2 & 2 & 4 \\
8 & 2 & 1 & 4 & 4 & 8 \\
8 & 2 & 4 & 1 & 4 & 8 \\
2 & 2 & 4 & 4 & 1 & 2 \\
4 & 4 & 8 & 8 & 2 & 1
\end{array}\right)\)
