Elliptic curves in class 16.1-b over 4.4.5744.1
Isogeny class 16.1-b contains
4 curves linked by isogenies of
degrees dividing 4.
Curve label |
Weierstrass Coefficients |
16.1-b1
| \( \bigl[a^{3} - 4 a - 1\) , \( a^{2} - a - 1\) , \( -a^{3} + a^{2} + 5 a\) , \( -39 a^{3} + 15 a^{2} + 144 a - 48\) , \( 144 a^{3} - 58 a^{2} - 562 a + 157\bigr] \)
|
16.1-b2
| \( \bigl[a^{3} - 4 a - 1\) , \( -a^{2} + a + 3\) , \( a^{2} - a - 1\) , \( 9 a^{3} - 7 a^{2} - 38 a - 19\) , \( -17 a^{3} + 25 a^{2} + 45 a + 13\bigr] \)
|
16.1-b3
| \( \bigl[a^{3} - 4 a - 1\) , \( -a^{2} + a + 3\) , \( a^{2} - a - 1\) , \( 4 a^{3} - 7 a^{2} - 8 a + 1\) , \( -9 a^{3} + 23 a^{2} + 2 a - 15\bigr] \)
|
16.1-b4
| \( \bigl[0\) , \( -2 a^{3} + a^{2} + 9 a + 1\) , \( 0\) , \( -8 a^{3} - 22 a^{2} - 8 a + 9\) , \( 50 a^{3} + 122 a^{2} + 39 a - 21\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrr}
1 & 4 & 2 & 4 \\
4 & 1 & 2 & 4 \\
2 & 2 & 1 & 2 \\
4 & 4 & 2 & 1
\end{array}\right)\)