Elliptic curves in class 4.2-b over 4.4.9225.1
Isogeny class 4.2-b contains
6 curves linked by isogenies of
degrees dividing 8.
| Curve label |
Weierstrass Coefficients |
| 4.2-b1
| \( \bigl[\frac{1}{4} a^{3} + a^{2} - \frac{1}{2} a - \frac{15}{4}\) , \( \frac{1}{4} a^{3} + a^{2} - \frac{3}{2} a - \frac{15}{4}\) , \( \frac{1}{4} a^{3} - \frac{3}{2} a + \frac{1}{4}\) , \( -69 a^{3} + 193 a^{2} + 546 a - 1356\) , \( 1285 a^{3} - 2709 a^{2} - 9407 a + 19721\bigr] \)
|
| 4.2-b2
| \( \bigl[\frac{1}{4} a^{3} + a^{2} - \frac{1}{2} a - \frac{15}{4}\) , \( -\frac{1}{4} a^{3} - a^{2} + \frac{1}{2} a + \frac{15}{4}\) , \( 1\) , \( -\frac{11}{4} a^{3} - 2 a^{2} + \frac{51}{2} a + \frac{117}{4}\) , \( -\frac{53}{4} a^{3} - 12 a^{2} + \frac{215}{2} a + \frac{467}{4}\bigr] \)
|
| 4.2-b3
| \( \bigl[a\) , \( \frac{1}{4} a^{3} + a^{2} - \frac{5}{2} a - \frac{15}{4}\) , \( 0\) , \( -\frac{1}{2} a^{3} + a^{2} + a - \frac{3}{2}\) , \( 0\bigr] \)
|
| 4.2-b4
| \( \bigl[a\) , \( \frac{1}{4} a^{3} + a^{2} - \frac{5}{2} a - \frac{15}{4}\) , \( 0\) , \( 2 a^{3} - 4 a^{2} - 4 a + 6\) , \( \frac{23}{2} a^{3} - 31 a^{2} - 10 a + \frac{107}{2}\bigr] \)
|
| 4.2-b5
| \( \bigl[\frac{1}{4} a^{3} - \frac{1}{2} a + \frac{1}{4}\) , \( -\frac{1}{4} a^{3} + \frac{5}{2} a + \frac{3}{4}\) , \( \frac{1}{4} a^{3} + a^{2} - \frac{1}{2} a - \frac{19}{4}\) , \( -\frac{141}{4} a^{3} + 76 a^{2} + \frac{521}{2} a - \frac{2193}{4}\) , \( 375 a^{3} - 826 a^{2} - 2759 a + 5942\bigr] \)
|
| 4.2-b6
| \( \bigl[1\) , \( \frac{1}{4} a^{3} - a^{2} - \frac{3}{2} a + \frac{21}{4}\) , \( a\) , \( \frac{1}{4} a^{3} - a^{2} - \frac{5}{2} a + \frac{37}{4}\) , \( \frac{5}{4} a^{3} - \frac{19}{2} a - \frac{15}{4}\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrrrr}
1 & 8 & 4 & 8 & 2 & 4 \\
8 & 1 & 2 & 4 & 4 & 8 \\
4 & 2 & 1 & 2 & 2 & 4 \\
8 & 4 & 2 & 1 & 4 & 8 \\
2 & 4 & 2 & 4 & 1 & 2 \\
4 & 8 & 4 & 8 & 2 & 1
\end{array}\right)\)
