Elliptic curves in class 49.1-a over 4.4.17725.1
Isogeny class 49.1-a contains
4 curves linked by isogenies of
degrees dividing 4.
Curve label |
Weierstrass Coefficients |
49.1-a1
| \( \bigl[a^{3} - 8 a - 7\) , \( -1\) , \( a^{2} - a - 6\) , \( -316 a^{3} + 1392 a^{2} + 609 a - 5812\) , \( -5945 a^{3} + 25549 a^{2} + 12413 a - 105480\bigr] \)
|
49.1-a2
| \( \bigl[a^{2} - 7\) , \( a^{3} - a^{2} - 8 a + 1\) , \( a^{3} - 8 a - 6\) , \( -271 a^{3} + 578 a^{2} + 1550 a - 2816\) , \( -2564 a^{3} + 15531 a^{2} + 9010 a - 93150\bigr] \)
|
49.1-a3
| \( \bigl[a^{2} - 7\) , \( a^{3} - a^{2} - 8 a + 1\) , \( a^{3} - 8 a - 6\) , \( -21 a^{3} + 23 a^{2} + 135 a - 66\) , \( -97 a^{3} + 260 a^{2} + 524 a - 1361\bigr] \)
|
49.1-a4
| \( \bigl[a^{2} - 7\) , \( a^{3} - a^{2} - 8 a + 1\) , \( a^{3} - 8 a - 6\) , \( -a^{3} + 8 a^{2} + 5 a - 41\) , \( 3 a^{3} + 2 a^{2} - 25 a - 31\bigr] \)
|
Rank: \( 1 \)
\(\left(\begin{array}{rrrr}
1 & 4 & 2 & 4 \\
4 & 1 & 2 & 4 \\
2 & 2 & 1 & 2 \\
4 & 4 & 2 & 1
\end{array}\right)\)