Elliptic curves in class 25.2-a over 4.4.4525.1
Isogeny class 25.2-a contains
12 curves linked by isogenies of
degrees dividing 24.
| Curve label |
Weierstrass Coefficients |
| 25.2-a1
| \( \bigl[\frac{1}{3} a^{3} + \frac{2}{3} a^{2} - \frac{7}{3} a - 4\) , \( \frac{1}{3} a^{3} + \frac{2}{3} a^{2} - \frac{10}{3} a - 5\) , \( 0\) , \( -20 a^{3} + 105 a^{2} + 70 a - 564\) , \( -238 a^{3} + 908 a^{2} + 924 a - 4429\bigr] \)
|
| 25.2-a2
| \( \bigl[\frac{1}{3} a^{3} + \frac{2}{3} a^{2} - \frac{7}{3} a - 4\) , \( \frac{1}{3} a^{3} + \frac{2}{3} a^{2} - \frac{10}{3} a - 5\) , \( 0\) , \( -\frac{10}{3} a^{3} + \frac{25}{3} a^{2} - \frac{5}{3} a - 74\) , \( 13 a^{3} - 25 a^{2} + 14 a + 245\bigr] \)
|
| 25.2-a3
| \( \bigl[\frac{1}{3} a^{3} + \frac{2}{3} a^{2} - \frac{7}{3} a - 4\) , \( \frac{1}{3} a^{3} + \frac{2}{3} a^{2} - \frac{10}{3} a - 5\) , \( 0\) , \( \frac{10}{3} a^{3} - \frac{25}{3} a^{2} + \frac{5}{3} a - 14\) , \( \frac{53}{3} a^{3} - \frac{155}{3} a^{2} + \frac{4}{3} a + 31\bigr] \)
|
| 25.2-a4
| \( \bigl[\frac{1}{3} a^{3} + \frac{2}{3} a^{2} - \frac{7}{3} a - 4\) , \( \frac{1}{3} a^{3} + \frac{2}{3} a^{2} - \frac{10}{3} a - 5\) , \( 0\) , \( -4\) , \( \frac{2}{3} a^{3} - \frac{5}{3} a^{2} + \frac{1}{3} a + 6\bigr] \)
|
| 25.2-a5
| \( \bigl[\frac{1}{3} a^{3} + \frac{2}{3} a^{2} - \frac{7}{3} a - 4\) , \( \frac{1}{3} a^{3} + \frac{2}{3} a^{2} - \frac{10}{3} a - 5\) , \( 0\) , \( 1\) , \( 0\bigr] \)
|
| 25.2-a6
| \( \bigl[\frac{1}{3} a^{3} + \frac{2}{3} a^{2} - \frac{7}{3} a - 3\) , \( 1\) , \( \frac{1}{3} a^{3} + \frac{2}{3} a^{2} - \frac{7}{3} a - 3\) , \( -\frac{20}{3} a^{3} + \frac{5}{3} a^{2} + \frac{125}{3} a - 50\) , \( \frac{73}{3} a^{3} - \frac{52}{3} a^{2} - \frac{445}{3} a + 165\bigr] \)
|
| 25.2-a7
| \( \bigl[\frac{1}{3} a^{3} + \frac{2}{3} a^{2} - \frac{7}{3} a - 3\) , \( 1\) , \( \frac{1}{3} a^{3} + \frac{2}{3} a^{2} - \frac{7}{3} a - 3\) , \( \frac{20}{3} a^{3} - \frac{5}{3} a^{2} - \frac{125}{3} a - 40\) , \( 37 a^{3} + 2 a^{2} - 235 a - 209\bigr] \)
|
| 25.2-a8
| \( \bigl[\frac{1}{3} a^{3} + \frac{2}{3} a^{2} - \frac{7}{3} a - 3\) , \( 1\) , \( \frac{1}{3} a^{3} + \frac{2}{3} a^{2} - \frac{7}{3} a - 3\) , \( -5\) , \( \frac{4}{3} a^{3} - \frac{1}{3} a^{2} - \frac{25}{3} a - 4\bigr] \)
|
| 25.2-a9
| \( \bigl[\frac{1}{3} a^{3} + \frac{2}{3} a^{2} - \frac{7}{3} a - 3\) , \( 1\) , \( \frac{1}{3} a^{3} + \frac{2}{3} a^{2} - \frac{7}{3} a - 3\) , \( 0\) , \( 0\bigr] \)
|
| 25.2-a10
| \( \bigl[\frac{1}{3} a^{3} + \frac{2}{3} a^{2} - \frac{7}{3} a - 3\) , \( 1\) , \( \frac{1}{3} a^{3} + \frac{2}{3} a^{2} - \frac{7}{3} a - 3\) , \( 5 a^{3} - 90 a^{2} - 10 a + 105\) , \( -19 a^{3} - 736 a^{2} + 114 a + 1008\bigr] \)
|
| 25.2-a11
| \( \bigl[\frac{1}{3} a^{3} - \frac{1}{3} a^{2} - \frac{1}{3} a\) , \( -\frac{1}{3} a^{3} - \frac{2}{3} a^{2} + \frac{4}{3} a + 3\) , \( \frac{1}{3} a^{3} - \frac{1}{3} a^{2} - \frac{1}{3} a\) , \( \frac{31}{3} a^{3} - \frac{142}{3} a^{2} - \frac{19}{3} a + 83\) , \( -\frac{880}{3} a^{3} + \frac{1594}{3} a^{2} + \frac{5065}{3} a - 2676\bigr] \)
|
| 25.2-a12
| \( \bigl[a + 1\) , \( \frac{1}{3} a^{3} - \frac{1}{3} a^{2} - \frac{4}{3} a - 1\) , \( \frac{1}{3} a^{3} + \frac{2}{3} a^{2} - \frac{4}{3} a - 4\) , \( \frac{28}{3} a^{3} + \frac{77}{3} a^{2} - \frac{214}{3} a - 170\) , \( -\frac{221}{3} a^{3} - \frac{598}{3} a^{2} - \frac{451}{3} a - 122\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrrrrrrrrrr}
1 & 8 & 2 & 4 & 8 & 24 & 6 & 12 & 24 & 12 & 4 & 3 \\
8 & 1 & 4 & 2 & 4 & 3 & 12 & 6 & 12 & 24 & 8 & 24 \\
2 & 4 & 1 & 2 & 4 & 12 & 3 & 6 & 12 & 6 & 2 & 6 \\
4 & 2 & 2 & 1 & 2 & 6 & 6 & 3 & 6 & 12 & 4 & 12 \\
8 & 4 & 4 & 2 & 1 & 12 & 12 & 6 & 3 & 24 & 8 & 24 \\
24 & 3 & 12 & 6 & 12 & 1 & 4 & 2 & 4 & 8 & 24 & 8 \\
6 & 12 & 3 & 6 & 12 & 4 & 1 & 2 & 4 & 2 & 6 & 2 \\
12 & 6 & 6 & 3 & 6 & 2 & 2 & 1 & 2 & 4 & 12 & 4 \\
24 & 12 & 12 & 6 & 3 & 4 & 4 & 2 & 1 & 8 & 24 & 8 \\
12 & 24 & 6 & 12 & 24 & 8 & 2 & 4 & 8 & 1 & 3 & 4 \\
4 & 8 & 2 & 4 & 8 & 24 & 6 & 12 & 24 & 3 & 1 & 12 \\
3 & 24 & 6 & 12 & 24 & 8 & 2 & 4 & 8 & 4 & 12 & 1
\end{array}\right)\)
