Elliptic curves in class 12.1-b over 4.4.18097.1
Isogeny class 12.1-b contains
6 curves linked by isogenies of
degrees dividing 8.
| Curve label |
Weierstrass Coefficients |
| 12.1-b1
| \( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - 1\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{7}{2} a - 2\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - 1\) , \( \frac{1}{2} a^{3} + \frac{3}{2} a^{2} - \frac{3}{2} a - 1\) , \( \frac{7}{2} a^{3} + \frac{11}{2} a^{2} - \frac{23}{2} a - 6\bigr] \)
|
| 12.1-b2
| \( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - 1\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{5}{2} a + 1\) , \( 1\) , \( \frac{29}{2} a^{3} + \frac{5}{2} a^{2} - \frac{173}{2} a - 37\) , \( -\frac{47}{2} a^{3} - \frac{9}{2} a^{2} + \frac{289}{2} a + 64\bigr] \)
|
| 12.1-b3
| \( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - 1\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{5}{2} a + 1\) , \( 1\) , \( -\frac{81}{2} a^{3} - \frac{105}{2} a^{2} + \frac{687}{2} a + 163\) , \( -\frac{135}{2} a^{3} - \frac{537}{2} a^{2} + \frac{1913}{2} a + 480\bigr] \)
|
| 12.1-b4
| \( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{3}{2} a + 2\) , \( -\frac{1}{2} a^{3} + \frac{1}{2} a^{2} + \frac{5}{2} a - 1\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{3}{2} a + 2\) , \( -103 a^{3} + 149 a^{2} + 651 a - 908\) , \( 1247 a^{3} - 1810 a^{2} - 7914 a + 11056\bigr] \)
|
| 12.1-b5
| \( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{3}{2} a + 2\) , \( -\frac{1}{2} a^{3} + \frac{1}{2} a^{2} + \frac{5}{2} a - 1\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{3}{2} a + 2\) , \( -23 a^{3} + 34 a^{2} + 141 a - 198\) , \( -110 a^{3} + 161 a^{2} + 691 a - 968\bigr] \)
|
| 12.1-b6
| \( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{5}{2} a + 3\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - 3\) , \( a^{3} - 4 a + 1\) , \( -\frac{1}{2} a^{3} - \frac{1}{2} a^{2} + \frac{7}{2} a - 1\) , \( -\frac{3}{2} a^{3} - \frac{3}{2} a^{2} + \frac{15}{2} a + 2\bigr] \)
|
Rank: \( 1 \)
\(\left(\begin{array}{rrrrrr}
1 & 2 & 4 & 8 & 4 & 8 \\
2 & 1 & 2 & 4 & 2 & 4 \\
4 & 2 & 1 & 8 & 4 & 8 \\
8 & 4 & 8 & 1 & 2 & 4 \\
4 & 2 & 4 & 2 & 1 & 2 \\
8 & 4 & 8 & 4 & 2 & 1
\end{array}\right)\)
