Elliptic curves in class 11.1-a over 3.3.1957.1
Isogeny class 11.1-a contains
6 curves linked by isogenies of
degrees dividing 8.
| Curve label |
Weierstrass Coefficients |
| 11.1-a1
| \( \bigl[a^{2} + a - 6\) , \( a^{2} - 7\) , \( a^{2} + a - 6\) , \( 51895 a^{2} + 99196 a - 178244\) , \( 33758168 a^{2} + 64528849 a - 115947554\bigr] \)
|
| 11.1-a2
| \( \bigl[1\) , \( -a^{2} + a + 6\) , \( a + 1\) , \( -185636 a^{2} - 354832 a + 637593\) , \( 100217800 a^{2} + 191566613 a - 344213187\bigr] \)
|
| 11.1-a3
| \( \bigl[1\) , \( -a^{2} - a + 7\) , \( a^{2} - 6\) , \( 182617 a^{2} + 349076 a - 627219\) , \( -278846719 a^{2} - 533016427 a + 957741374\bigr] \)
|
| 11.1-a4
| \( \bigl[1\) , \( -a^{2} - a + 7\) , \( a^{2} - 6\) , \( -32083 a^{2} - 61324 a + 110201\) , \( 6318353 a^{2} + 12077553 a - 21701344\bigr] \)
|
| 11.1-a5
| \( \bigl[1\) , \( -a^{2} - a + 7\) , \( a^{2} - 6\) , \( -134683 a^{2} - 257444 a + 462596\) , \( -55487530 a^{2} - 106064597 a + 190580341\bigr] \)
|
| 11.1-a6
| \( \bigl[1\) , \( -a^{2} - a + 7\) , \( a^{2} - 6\) , \( -2093583 a^{2} - 4001884 a + 7190731\) , \( -3794498373 a^{2} - 7253196207 a + 13032780528\bigr] \)
|
Rank \(r\) satisfies \(0 \le r \le 2\)
\(\left(\begin{array}{rrrrrr}
1 & 4 & 8 & 2 & 4 & 8 \\
4 & 1 & 8 & 2 & 4 & 8 \\
8 & 8 & 1 & 4 & 2 & 4 \\
2 & 2 & 4 & 1 & 2 & 4 \\
4 & 4 & 2 & 2 & 1 & 2 \\
8 & 8 & 4 & 4 & 2 & 1
\end{array}\right)\)
