Elliptic curves in class 8.1-b over 3.3.1849.1
Isogeny class 8.1-b contains
6 curves linked by isogenies of
degrees dividing 8.
| Curve label |
Weierstrass Coefficients |
| 8.1-b1
| \( \bigl[1\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - 4\) , \( \frac{1}{2} a^{2} + \frac{1}{2} a - 5\) , \( -\frac{3505619809}{2} a^{2} - \frac{8373456057}{2} a - 1912026652\) , \( -\frac{258349956520917}{2} a^{2} - \frac{1005318188491443}{2} a - 260302759228368\bigr] \)
|
| 8.1-b2
| \( \bigl[1\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - 4\) , \( \frac{1}{2} a^{2} + \frac{1}{2} a - 5\) , \( -\frac{219683109}{2} a^{2} - \frac{521078557}{2} a - 118695812\) , \( -\frac{4044776198393}{2} a^{2} - \frac{15678187411863}{2} a - 4056508189528\bigr] \)
|
| 8.1-b3
| \( \bigl[1\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - 4\) , \( \frac{1}{2} a^{2} + \frac{1}{2} a - 5\) , \( -758 a^{2} - 2697 a - 1366\) , \( -2163 a^{2} - 7356 a - 3714\bigr] \)
|
| 8.1-b4
| \( \bigl[1\) , \( -a + 1\) , \( 0\) , \( -136930219333 a^{2} - 480088861360 a - 243486540062\) , \( -120359968985897693 a^{2} - 421678979526764474 a - 213829021937955940\bigr] \)
|
| 8.1-b5
| \( \bigl[1\) , \( a + 1\) , \( 0\) , \( -965526 a^{2} + 3725008 a + 2656418\) , \( -1189625710 a^{2} + 4621159606 a + 3292395148\bigr] \)
|
| 8.1-b6
| \( \bigl[1\) , \( -\frac{1}{2} a^{2} + \frac{3}{2} a + 5\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - 4\) , \( -93008767623 a^{2} + 361640039403 a + 257620962662\) , \( -44749942048306662 a^{2} + 173998336065881803 a + 123950928971976024\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrrrr}
1 & 2 & 8 & 4 & 4 & 8 \\
2 & 1 & 4 & 2 & 2 & 4 \\
8 & 4 & 1 & 8 & 2 & 4 \\
4 & 2 & 8 & 1 & 4 & 8 \\
4 & 2 & 2 & 4 & 1 & 2 \\
8 & 4 & 4 & 8 & 2 & 1
\end{array}\right)\)
