Elliptic curves in class 4.1-b over 3.3.1849.1
Isogeny class 4.1-b contains
6 curves linked by isogenies of
degrees dividing 8.
| Curve label |
Weierstrass Coefficients |
| 4.1-b1
| \( \bigl[1\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - 4\) , \( \frac{1}{2} a^{2} + \frac{1}{2} a - 5\) , \( -\frac{13872525}{2} a^{2} - \frac{48599719}{2} a - 12322069\) , \( -43257956975 a^{2} - 151545930933 a - 76846550118\bigr] \)
|
| 4.1-b2
| \( \bigl[1\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - 4\) , \( \frac{1}{2} a^{2} + \frac{1}{2} a - 5\) , \( -\frac{872185}{2} a^{2} - \frac{3055529}{2} a - 774699\) , \( -667920965 a^{2} - 2339932619 a - 1186542914\bigr] \)
|
| 4.1-b3
| \( \bigl[1\) , \( -a + 1\) , \( 0\) , \( 90318539 a^{2} + 316413625 a + 160448357\) , \( -118907236571270 a^{2} - 416568629695857 a - 211235378469329\bigr] \)
|
| 4.1-b4
| \( \bigl[1\) , \( a + 1\) , \( 0\) , \( -41 a^{2} - 144 a - 73\) , \( 282 a^{2} + 988 a + 501\bigr] \)
|
| 4.1-b5
| \( \bigl[1\) , \( -\frac{1}{2} a^{2} + \frac{3}{2} a + 5\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - 4\) , \( -42 a^{2} + 162 a + 123\) , \( -\frac{755}{2} a^{2} + \frac{2935}{2} a + 1045\bigr] \)
|
| 4.1-b6
| \( \bigl[1\) , \( -\frac{1}{2} a^{2} + \frac{3}{2} a + 6\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - 5\) , \( -\frac{3879932424665305}{2} a^{2} - \frac{13592596885275349}{2} a - 3446295691466837\) , \( 202229635727891203882007 a^{2} + 708472626799016062597209 a + 359255289017598093575882\bigr] \)
|
Rank: \( 1 \)
\(\left(\begin{array}{rrrrrr}
1 & 2 & 4 & 4 & 8 & 8 \\
2 & 1 & 2 & 2 & 4 & 4 \\
4 & 2 & 1 & 4 & 8 & 8 \\
4 & 2 & 4 & 1 & 2 & 2 \\
8 & 4 & 8 & 2 & 1 & 4 \\
8 & 4 & 8 & 2 & 4 & 1
\end{array}\right)\)
