Elliptic curves in class 3.3-b over 4.4.11661.1
Isogeny class 3.3-b contains
4 curves linked by isogenies of
degrees dividing 6.
| Curve label |
Weierstrass Coefficients |
| 3.3-b1
| \( \bigl[a^{3} - 5 a - 1\) , \( a^{3} - a^{2} - 3 a\) , \( 0\) , \( -20 a^{3} - 4 a^{2} + 64 a + 28\) , \( -121 a^{3} - 49 a^{2} + 339 a + 157\bigr] \)
|
| 3.3-b2
| \( \bigl[a^{3} - 5 a - 1\) , \( -a^{2} + a + 3\) , \( a^{2} - a - 3\) , \( 45 a^{3} - 174 a^{2} + 115 a + 82\) , \( -491 a^{3} + 1770 a^{2} - 903 a - 929\bigr] \)
|
| 3.3-b3
| \( \bigl[a^{3} - 4 a - 1\) , \( a^{3} - 4 a - 3\) , \( a^{3} - 4 a - 2\) , \( -206 a^{3} + 525 a^{2} + 583 a - 1347\) , \( -3045 a^{3} + 7562 a^{2} + 8619 a - 19380\bigr] \)
|
| 3.3-b4
| \( \bigl[a + 1\) , \( -a^{3} + 2 a^{2} + 2 a - 3\) , \( a^{3} - 4 a - 1\) , \( -34 a^{3} + 80 a^{2} + 97 a - 201\) , \( 206 a^{3} - 511 a^{2} - 584 a + 1308\bigr] \)
|
Rank: \( 1 \)
\(\left(\begin{array}{rrrr}
1 & 3 & 6 & 2 \\
3 & 1 & 2 & 6 \\
6 & 2 & 1 & 3 \\
2 & 6 & 3 & 1
\end{array}\right)\)
