Elliptic curves in class 12.1-a over 4.4.18097.1
Isogeny class 12.1-a contains
6 curves linked by isogenies of
degrees dividing 8.
| Curve label |
Weierstrass Coefficients |
| 12.1-a1
| \( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{3}{2} a - 2\) , \( a^{2} + a - 4\) , \( a\) , \( \frac{7}{2} a^{3} - \frac{23}{2} a^{2} - \frac{57}{2} a + 53\) , \( -\frac{43}{2} a^{3} - \frac{195}{2} a^{2} - \frac{17}{2} a + 251\bigr] \)
|
| 12.1-a2
| \( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - 1\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{7}{2} a + 3\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - 2\) , \( 53 a^{3} - 144 a^{2} + 10 a + 21\) , \( -\frac{1561}{2} a^{3} + \frac{4685}{2} a^{2} - \frac{1035}{2} a - 858\bigr] \)
|
| 12.1-a3
| \( \bigl[a^{3} - 5 a + 1\) , \( a^{3} - 6 a + 1\) , \( a^{3} - 4 a\) , \( 4 a^{3} - 8 a^{2} - 5 a + 8\) , \( -5 a^{3} + 23 a^{2} - 18 a - 8\bigr] \)
|
| 12.1-a4
| \( \bigl[a + 1\) , \( a^{2} - 3\) , \( a^{3} - 4 a\) , \( -a^{3} + 2 a^{2} + 7 a - 10\) , \( 4 a^{3} - 5 a^{2} - 24 a + 28\bigr] \)
|
| 12.1-a5
| \( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{3}{2} a + 2\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - 2\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{3}{2} a + 3\) , \( -\frac{3}{2} a^{3} - \frac{1}{2} a^{2} + \frac{13}{2} a - 2\) , \( -4 a^{3} - 5 a^{2} + 12 a + 3\bigr] \)
|
| 12.1-a6
| \( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{3}{2} a + 2\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - 2\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{3}{2} a + 3\) , \( -\frac{13}{2} a^{3} - \frac{11}{2} a^{2} + \frac{53}{2} a - 2\) , \( 7 a^{3} + 8 a^{2} - 24 a - 5\bigr] \)
|
Rank: \( 1 \)
\(\left(\begin{array}{rrrrrr}
1 & 4 & 2 & 8 & 4 & 8 \\
4 & 1 & 2 & 8 & 4 & 8 \\
2 & 2 & 1 & 4 & 2 & 4 \\
8 & 8 & 4 & 1 & 2 & 4 \\
4 & 4 & 2 & 2 & 1 & 2 \\
8 & 8 & 4 & 4 & 2 & 1
\end{array}\right)\)
