Elliptic curves in class 16.1-b over 4.4.2777.1
Isogeny class 16.1-b contains
4 curves linked by isogenies of
degrees dividing 14.
Curve label |
Weierstrass Coefficients |
16.1-b1
| \( \bigl[a^{2} - a - 1\) , \( -a^{3} + 2 a^{2} + a - 3\) , \( a^{2} - a - 1\) , \( 1375 a^{3} - 489 a^{2} - 5280 a - 3053\) , \( 42544 a^{3} - 11186 a^{2} - 169964 a - 97423\bigr] \)
|
16.1-b2
| \( \bigl[a^{2} - 1\) , \( -a^{3} + 3 a\) , \( a\) , \( -4 a^{3} + 7 a^{2} + 11 a - 12\) , \( 3 a^{3} - 3 a^{2} - 7 a + 6\bigr] \)
|
16.1-b3
| \( \bigl[a^{3} - a^{2} - 3 a + 1\) , \( -a^{3} + a^{2} + 2 a - 1\) , \( a^{3} - a^{2} - 3 a + 1\) , \( 3 a^{3} - 3 a^{2} - 10 a + 3\) , \( -a^{3} + a^{2} + 3 a - 1\bigr] \)
|
16.1-b4
| \( \bigl[1\) , \( -a^{3} + 2 a^{2} + 2 a - 3\) , \( a^{2} - a - 1\) , \( 559 a^{3} - 1437 a^{2} - 22 a + 670\) , \( 15729 a^{3} - 39584 a^{2} - 3004 a + 20573\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrr}
1 & 7 & 14 & 2 \\
7 & 1 & 2 & 14 \\
14 & 2 & 1 & 7 \\
2 & 14 & 7 & 1
\end{array}\right)\)