Elliptic curves in class 25.1-c over 4.4.12400.1
Isogeny class 25.1-c contains
4 curves linked by isogenies of
degrees dividing 6.
| Curve label |
Weierstrass Coefficients |
| 25.1-c1
| \( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{7}{2} a - \frac{7}{2}\) , \( \frac{1}{2} a^{2} - \frac{7}{2}\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - \frac{7}{2}\) , \( -a^{3} + \frac{5}{2} a^{2} + 3 a - \frac{21}{2}\) , \( -11 a^{3} + \frac{61}{2} a^{2} + 41 a - \frac{231}{2}\bigr] \)
|
| 25.1-c2
| \( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{7}{2} a - \frac{7}{2}\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{9}{2} a - \frac{7}{2}\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - \frac{7}{2}\) , \( \frac{3}{2} a^{3} + \frac{5}{2} a^{2} - \frac{17}{2} a - \frac{21}{2}\) , \( 11 a^{3} + \frac{61}{2} a^{2} - 42 a - \frac{231}{2}\bigr] \)
|
| 25.1-c3
| \( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{7}{2} a - \frac{7}{2}\) , \( \frac{1}{2} a^{2} - \frac{7}{2}\) , \( a\) , \( -\frac{5}{2} a^{3} - 6 a^{2} + \frac{37}{2} a + 42\) , \( -\frac{9}{2} a^{3} - 12 a^{2} + \frac{45}{2} a + 55\bigr] \)
|
| 25.1-c4
| \( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{7}{2} a - \frac{7}{2}\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{9}{2} a - \frac{7}{2}\) , \( a\) , \( 2 a^{3} - 6 a^{2} - 15 a + 42\) , \( \frac{9}{2} a^{3} - 12 a^{2} - \frac{45}{2} a + 55\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrr}
1 & 6 & 2 & 3 \\
6 & 1 & 3 & 2 \\
2 & 3 & 1 & 6 \\
3 & 2 & 6 & 1
\end{array}\right)\)
