Elliptic curves in class 3.1-b over 4.4.18097.1
Isogeny class 3.1-b contains
6 curves linked by isogenies of
degrees dividing 8.
| Curve label |
Weierstrass Coefficients |
| 3.1-b1
| \( \bigl[a^{3} - 5 a + 1\) , \( 1\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{3}{2} a + 2\) , \( -226 a^{3} + 332 a^{2} + 1435 a - 2025\) , \( 4202 a^{3} - 6092 a^{2} - 26640 a + 37153\bigr] \)
|
| 3.1-b2
| \( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{5}{2} a + 2\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - 3\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{3}{2} a + 3\) , \( \frac{3}{2} a^{3} - \frac{17}{2} a^{2} + \frac{23}{2} a + 2\) , \( -9 a^{3} + 31 a^{2} - 15 a - 17\bigr] \)
|
| 3.1-b3
| \( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{3}{2} a + 2\) , \( a^{2} - a - 3\) , \( a\) , \( -2 a^{3} + 4 a^{2} + 3 a - 3\) , \( -2 a^{3} + 6 a^{2} - 3 a - 5\bigr] \)
|
| 3.1-b4
| \( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{5}{2} a + 3\) , \( a^{2} - 4\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{3}{2} a - 2\) , \( 2 a^{3} - 4 a^{2} - 12 a - 2\) , \( 68 a^{3} + 89 a^{2} - 210 a - 107\bigr] \)
|
| 3.1-b5
| \( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{5}{2} a + 3\) , \( a^{2} - 4\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{3}{2} a - 2\) , \( -3 a^{3} - 9 a^{2} - 2 a + 3\) , \( 21 a^{3} + 28 a^{2} - 75 a - 38\bigr] \)
|
| 3.1-b6
| \( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{5}{2} a + 3\) , \( a^{2} - 4\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{3}{2} a - 2\) , \( -\frac{1}{2} a^{3} - \frac{3}{2} a^{2} + \frac{1}{2} a + 3\) , \( -\frac{3}{2} a^{3} - \frac{5}{2} a^{2} + \frac{9}{2} a + 2\bigr] \)
|
Rank: \( 1 \)
\(\left(\begin{array}{rrrrrr}
1 & 8 & 8 & 4 & 2 & 4 \\
8 & 1 & 4 & 8 & 4 & 2 \\
8 & 4 & 1 & 8 & 4 & 2 \\
4 & 8 & 8 & 1 & 2 & 4 \\
2 & 4 & 4 & 2 & 1 & 2 \\
4 & 2 & 2 & 4 & 2 & 1
\end{array}\right)\)
