Rank: \( 1 \)
\(\left(\begin{array}{rrrrrr}
1 & 2 & 4 & 8 & 4 & 8 \\
2 & 1 & 2 & 4 & 2 & 4 \\
4 & 2 & 1 & 8 & 4 & 8 \\
8 & 4 & 8 & 1 & 2 & 4 \\
4 & 2 & 4 & 2 & 1 & 2 \\
8 & 4 & 8 & 4 & 2 & 1
\end{array}\right)\)
Elliptic curves in class 4.1-b over 6.6.1312625.1
Isogeny class 4.1-b contains
6 curves linked by isogenies of
degrees dividing 8.
| Curve label |
Weierstrass Coefficients |
| 4.1-b1
| \( \bigl[a^{2} + a - 2\) , \( a^{5} - 6 a^{3} - a^{2} + 7 a + 4\) , \( a^{4} - 5 a^{2} + a + 5\) , \( 69 a^{5} - 80 a^{4} - 493 a^{3} + 552 a^{2} + 835 a - 961\) , \( -828 a^{5} + 909 a^{4} + 5711 a^{3} - 6264 a^{2} - 9351 a + 10552\bigr] \)
|
| 4.1-b2
| \( \bigl[a^{2} + a - 2\) , \( a^{5} - 6 a^{3} - a^{2} + 7 a + 4\) , \( a^{4} - 5 a^{2} + a + 5\) , \( 4 a^{5} - 5 a^{4} - 28 a^{3} + 32 a^{2} + 45 a - 51\) , \( -7 a^{5} + 7 a^{4} + 47 a^{3} - 49 a^{2} - 75 a + 82\bigr] \)
|
| 4.1-b3
| \( \bigl[-a^{5} + 7 a^{3} + a^{2} - 11 a - 1\) , \( a^{4} - a^{3} - 4 a^{2} + 4 a + 1\) , \( a^{3} - 3 a + 2\) , \( 4 a^{5} - 6 a^{4} - 16 a^{3} + 26 a^{2} - 4 a + 1\) , \( -5 a^{5} + 17 a^{4} + 8 a^{3} - 69 a^{2} + 50 a + 5\bigr] \)
|
| 4.1-b4
| \( \bigl[a^{5} + a^{4} - 6 a^{3} - 4 a^{2} + 8 a + 2\) , \( -a^{5} + a^{4} + 6 a^{3} - 4 a^{2} - 9 a + 2\) , \( a^{5} - 6 a^{3} + 8 a\) , \( -3 a^{5} - 2 a^{4} + 11 a^{3} + 3 a^{2} - 10 a + 3\) , \( -19 a^{5} - 21 a^{4} + 85 a^{3} + 54 a^{2} - 101 a - 7\bigr] \)
|
| 4.1-b5
| \( \bigl[a^{4} - 5 a^{2} + a + 5\) , \( 3 a^{5} + a^{4} - 20 a^{3} - 5 a^{2} + 31 a + 3\) , \( a^{4} - 4 a^{2} + 2\) , \( 3 a^{5} - 3 a^{4} - 11 a^{3} + 4 a^{2} + 7 a + 10\) , \( 4 a^{5} - 12 a^{4} - a^{3} + 31 a^{2} - 29 a + 7\bigr] \)
|
| 4.1-b6
| \( \bigl[a^{2} - 2\) , \( a^{5} + a^{4} - 8 a^{3} - 4 a^{2} + 14 a\) , \( a^{4} - 4 a^{2} + 1\) , \( -3 a^{5} + 25 a^{3} + 17 a^{2} - 35 a - 27\) , \( -158 a^{5} - 101 a^{4} + 940 a^{3} + 422 a^{2} - 1250 a - 147\bigr] \)
|
