Elliptic curves in class 3.1-a over 4.4.18097.1
Isogeny class 3.1-a contains
6 curves linked by isogenies of
degrees dividing 8.
| Curve label |
Weierstrass Coefficients |
| 3.1-a1
| \( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{3}{2} a - 1\) , \( a^{2} + a - 3\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - 2\) , \( -10 a^{3} + 43 a^{2} - 20 a - 31\) , \( \frac{4623}{2} a^{3} - \frac{16427}{2} a^{2} + \frac{8359}{2} a + 3763\bigr] \)
|
| 3.1-a2
| \( \bigl[a^{3} - 5 a + 1\) , \( -a^{3} + 6 a\) , \( a\) , \( -6 a^{3} - 6 a^{2} + 28 a + 14\) , \( \frac{3}{2} a^{3} + \frac{11}{2} a^{2} + \frac{9}{2} a + 1\bigr] \)
|
| 3.1-a3
| \( \bigl[1\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{7}{2} a - 1\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{3}{2} a - 1\) , \( \frac{47}{2} a^{3} + \frac{27}{2} a^{2} - \frac{311}{2} a - 101\) , \( 122 a^{3} + 56 a^{2} - 797 a - 434\bigr] \)
|
| 3.1-a4
| \( \bigl[1\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{7}{2} a - 1\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{3}{2} a - 1\) , \( 21 a^{3} + 11 a^{2} - 138 a - 81\) , \( \frac{337}{2} a^{3} + \frac{161}{2} a^{2} - \frac{2201}{2} a - 619\bigr] \)
|
| 3.1-a5
| \( \bigl[1\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{7}{2} a - 1\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{3}{2} a - 1\) , \( a^{3} + a^{2} - 8 a - 6\) , \( -a^{3} - a^{2} + 4 a + 1\bigr] \)
|
| 3.1-a6
| \( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{5}{2} a + 3\) , \( -a^{3} + 4 a + 1\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - 2\) , \( 2 a^{3} - 2 a^{2} - 15 a + 23\) , \( \frac{3}{2} a^{3} - \frac{5}{2} a^{2} - \frac{27}{2} a + 18\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrrrr}
1 & 8 & 2 & 4 & 4 & 8 \\
8 & 1 & 4 & 8 & 2 & 4 \\
2 & 4 & 1 & 2 & 2 & 4 \\
4 & 8 & 2 & 1 & 4 & 8 \\
4 & 2 & 2 & 4 & 1 & 2 \\
8 & 4 & 4 & 8 & 2 & 1
\end{array}\right)\)
