Elliptic curves in class 8.1-b over 4.4.15188.1
Isogeny class 8.1-b contains
8 curves linked by isogenies of
degrees dividing 12.
| Curve label |
Weierstrass Coefficients |
| 8.1-b1
| \( \bigl[\frac{1}{2} a^{3} - \frac{5}{2} a - 2\) , \( a\) , \( 0\) , \( 10 a^{3} + 13 a^{2} - 79 a - 130\) , \( 5 a^{3} - 72 a^{2} - 29 a + 338\bigr] \)
|
| 8.1-b2
| \( \bigl[\frac{1}{2} a^{3} - \frac{5}{2} a - 2\) , \( -a^{2} + 5\) , \( a + 1\) , \( -\frac{167}{2} a^{3} - 176 a^{2} + \frac{87}{2} a + 57\) , \( -\frac{4019}{2} a^{3} - 4204 a^{2} + \frac{2139}{2} a + 1300\bigr] \)
|
| 8.1-b3
| \( \bigl[\frac{1}{2} a^{3} - \frac{5}{2} a - 2\) , \( -a^{2} + 5\) , \( a + 1\) , \( -221 a^{3} - 421 a^{2} + 186 a + 92\) , \( 5205 a^{3} + 10808 a^{2} - 2894 a - 3249\bigr] \)
|
| 8.1-b4
| \( \bigl[a + 1\) , \( a^{2} - 5\) , \( a + 1\) , \( -9 a^{3} + 4 a^{2} + 26 a - 59\) , \( -9 a^{3} - 159 a^{2} - 152 a + 339\bigr] \)
|
| 8.1-b5
| \( \bigl[a + 1\) , \( a^{2} - 5\) , \( a + 1\) , \( a^{3} - a^{2} - 4 a + 6\) , \( a^{2} + a - 3\bigr] \)
|
| 8.1-b6
| \( \bigl[\frac{1}{2} a^{3} - a^{2} - \frac{3}{2} a + 2\) , \( a + 1\) , \( a + 1\) , \( -\frac{3}{2} a^{3} + \frac{9}{2} a - 2\) , \( \frac{1}{2} a^{3} + a^{2} - \frac{3}{2} a\bigr] \)
|
| 8.1-b7
| \( \bigl[\frac{1}{2} a^{3} - a^{2} - \frac{3}{2} a + 2\) , \( -a^{2} + a + 4\) , \( \frac{1}{2} a^{3} - \frac{7}{2} a - 1\) , \( -\frac{63}{2} a^{3} + 46 a^{2} + \frac{393}{2} a - 120\) , \( -\frac{333}{2} a^{3} + 248 a^{2} + \frac{2087}{2} a - 678\bigr] \)
|
| 8.1-b8
| \( \bigl[\frac{1}{2} a^{3} - a^{2} - \frac{3}{2} a + 2\) , \( -a^{2} + 5\) , \( \frac{1}{2} a^{3} - a^{2} - \frac{3}{2} a + 2\) , \( -296 a^{3} + 122 a^{2} + 2140 a + 965\) , \( 5869 a^{3} - 2354 a^{2} - 42492 a - 19581\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrrrrrr}
1 & 2 & 4 & 4 & 12 & 6 & 3 & 12 \\
2 & 1 & 2 & 2 & 6 & 3 & 6 & 6 \\
4 & 2 & 1 & 4 & 12 & 6 & 12 & 3 \\
4 & 2 & 4 & 1 & 3 & 6 & 12 & 12 \\
12 & 6 & 12 & 3 & 1 & 2 & 4 & 4 \\
6 & 3 & 6 & 6 & 2 & 1 & 2 & 2 \\
3 & 6 & 12 & 12 & 4 & 2 & 1 & 4 \\
12 & 6 & 3 & 12 & 4 & 2 & 4 & 1
\end{array}\right)\)
