Elliptic curves in class 4.2-b over 3.3.1849.1
Isogeny class 4.2-b contains
6 curves linked by isogenies of
degrees dividing 8.
| Curve label |
Weierstrass Coefficients |
| 4.2-b1
| \( \bigl[1\) , \( \frac{1}{2} a^{2} - \frac{3}{2} a - 6\) , \( 1\) , \( -\frac{187}{2} a^{2} + \frac{725}{2} a + 265\) , \( 728 a^{2} - 2830 a - 2020\bigr] \)
|
| 4.2-b2
| \( \bigl[1\) , \( -\frac{1}{2} a^{2} - \frac{1}{2} a + 4\) , \( 1\) , \( 1035 a^{2} - 3935 a - 2806\) , \( 38047 a^{2} - 148183 a - 105534\bigr] \)
|
| 4.2-b3
| \( \bigl[1\) , \( -\frac{1}{2} a^{2} - \frac{1}{2} a + 5\) , \( 0\) , \( -139377851988054126331856 a^{2} - 488283492971561316848717 a - 247600853942073873231157\) , \( -\frac{1073992586713366267174174192865201037}{2} a^{2} - \frac{3762526428595782931371840513849977487}{2} a - 953958888749691934481770602093876513\bigr] \)
|
| 4.2-b4
| \( \bigl[1\) , \( -\frac{1}{2} a^{2} + \frac{3}{2} a + 5\) , \( 0\) , \( -1172779547969 a^{2} - 4108607544166 a - 2083410049876\) , \( -\frac{6013628427348503335}{2} a^{2} - \frac{21067590381508211477}{2} a - 5341521312975315674\bigr] \)
|
| 4.2-b5
| \( \bigl[1\) , \( -\frac{1}{2} a^{2} + \frac{3}{2} a + 5\) , \( 0\) , \( -\frac{146715161753}{2} a^{2} - \frac{513988346287}{2} a - 130317689706\) , \( -46902274759853089 a^{2} - 164313097248878730 a - 83320578676737960\bigr] \)
|
| 4.2-b6
| \( \bigl[1\) , \( -\frac{1}{2} a^{2} - \frac{1}{2} a + 6\) , \( 1\) , \( -8365385 a^{2} + 32526591 a + 23170931\) , \( 38152217234 a^{2} - 148344824870 a - 105676176364\bigr] \)
|
Rank: \( 1 \)
\(\left(\begin{array}{rrrrrr}
1 & 2 & 4 & 4 & 2 & 2 \\
2 & 1 & 8 & 8 & 4 & 4 \\
4 & 8 & 1 & 4 & 2 & 8 \\
4 & 8 & 4 & 1 & 2 & 8 \\
2 & 4 & 2 & 2 & 1 & 4 \\
2 & 4 & 8 & 8 & 4 & 1
\end{array}\right)\)
