Elliptic curves in class 97.1-a over 5.5.24217.1
Isogeny class 97.1-a contains
4 curves linked by isogenies of
degrees dividing 4.
Curve label |
Weierstrass Coefficients |
97.1-a1
| \( \bigl[-a^{4} + a^{3} + 5 a^{2} - 3 a - 2\) , \( a^{3} - a^{2} - 4 a\) , \( a^{4} - 4 a^{2} + a\) , \( -2 a^{4} + 2 a^{3} + 9 a^{2} - 10 a - 5\) , \( -a^{2} - a - 1\bigr] \)
|
97.1-a2
| \( \bigl[-a^{4} + a^{3} + 5 a^{2} - 3 a - 2\) , \( a^{3} - a^{2} - 4 a\) , \( a^{4} - 4 a^{2} + a\) , \( 13 a^{4} + 22 a^{3} - 51 a^{2} - 110 a - 45\) , \( 72 a^{4} + 75 a^{3} - 298 a^{2} - 393 a - 125\bigr] \)
|
97.1-a3
| \( \bigl[a + 1\) , \( 2 a^{4} - a^{3} - 9 a^{2} + 4 a + 2\) , \( a^{4} - 4 a^{2} + a\) , \( 5 a^{4} + 5 a^{3} - 25 a^{2} - 21 a - 5\) , \( 222 a^{4} - 145 a^{3} - 1003 a^{2} + 419 a + 280\bigr] \)
|
97.1-a4
| \( \bigl[-a^{4} + a^{3} + 5 a^{2} - 2 a - 2\) , \( 3 a^{4} - a^{3} - 14 a^{2} + 2 a + 4\) , \( -a^{4} + a^{3} + 5 a^{2} - 3 a - 2\) , \( -242 a^{4} + 89 a^{3} + 1173 a^{2} - 192 a - 659\) , \( -1145 a^{4} + 417 a^{3} + 5555 a^{2} - 907 a - 3091\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrr}
1 & 2 & 4 & 4 \\
2 & 1 & 2 & 2 \\
4 & 2 & 1 & 4 \\
4 & 2 & 4 & 1
\end{array}\right)\)