Elliptic curves in class 16.1-a over 4.4.14272.1
Isogeny class 16.1-a contains
4 curves linked by isogenies of
degrees dividing 4.
Curve label |
Weierstrass Coefficients |
16.1-a1
| \( \bigl[0\) , \( -a^{2} + 2 a + 3\) , \( 0\) , \( a^{2} - 2 a - 4\) , \( 0\bigr] \)
|
16.1-a2
| \( \bigl[a^{3} - 2 a^{2} - 4 a + 1\) , \( 2 a^{3} - 5 a^{2} - 7 a + 5\) , \( a^{3} - 2 a^{2} - 4 a + 1\) , \( 10 a^{3} - 30 a^{2} - 17 a + 26\) , \( 8 a^{3} - 24 a^{2} - 14 a + 23\bigr] \)
|
16.1-a3
| \( \bigl[a^{3} - 3 a^{2} - a + 4\) , \( -a^{3} + 3 a^{2} + a - 4\) , \( 2 a^{3} - 5 a^{2} - 5 a + 5\) , \( -3 a^{3} + 8 a^{2} + 6 a - 9\) , \( -15 a^{3} + 50 a^{2} + 5 a - 34\bigr] \)
|
16.1-a4
| \( \bigl[2 a^{3} - 5 a^{2} - 5 a + 5\) , \( -a^{2} + a + 2\) , \( 0\) , \( 38 a^{3} - 104 a^{2} - 116 a + 163\) , \( 208 a^{3} - 565 a^{2} - 635 a + 872\bigr] \)
|
Rank: \( 2 \)
\(\left(\begin{array}{rrrr}
1 & 2 & 2 & 2 \\
2 & 1 & 4 & 4 \\
2 & 4 & 1 & 4 \\
2 & 4 & 4 & 1
\end{array}\right)\)