Isogeny class 20.3-b contains
4 curves linked by isogenies of
degrees dividing 4.
| Curve label |
Weierstrass Coefficients |
| 20.3-b1
| \( \bigl[-\frac{1}{8} a^{3} + \frac{17}{8} a + \frac{3}{2}\) , \( \frac{1}{8} a^{3} + \frac{1}{2} a^{2} - \frac{21}{8} a - \frac{7}{2}\) , \( \frac{1}{8} a^{3} + \frac{1}{2} a^{2} - \frac{13}{8} a - \frac{7}{2}\) , \( -\frac{917}{8} a^{3} + \frac{273}{2} a^{2} + \frac{10657}{8} a - \frac{3185}{2}\) , \( \frac{479}{2} a^{3} - 279 a^{2} - \frac{5549}{2} a + 3204\bigr] \)
|
| 20.3-b2
| \( \bigl[-\frac{1}{8} a^{3} + \frac{17}{8} a + \frac{3}{2}\) , \( \frac{1}{8} a^{3} + \frac{1}{2} a^{2} - \frac{21}{8} a - \frac{7}{2}\) , \( \frac{1}{8} a^{3} + \frac{1}{2} a^{2} - \frac{13}{8} a - \frac{7}{2}\) , \( -84 a^{3} + 99 a^{2} + 974 a - 1145\) , \( \frac{5753}{4} a^{3} - 1689 a^{2} - \frac{66873}{4} a + 19634\bigr] \)
|
| 20.3-b3
| \( \bigl[\frac{1}{2} a^{2} - \frac{1}{2} a - 3\) , \( \frac{1}{8} a^{3} - \frac{1}{2} a^{2} - \frac{13}{8} a + \frac{7}{2}\) , \( -\frac{1}{8} a^{3} + \frac{17}{8} a + \frac{1}{2}\) , \( -\frac{3}{4} a^{3} + \frac{31}{4} a + 4\) , \( \frac{5}{8} a^{3} - 3 a^{2} - \frac{61}{8} a + \frac{67}{2}\bigr] \)
|
| 20.3-b4
| \( \bigl[\frac{1}{2} a^{2} - \frac{1}{2} a - 3\) , \( \frac{1}{8} a^{3} - \frac{1}{2} a^{2} - \frac{13}{8} a + \frac{7}{2}\) , \( -\frac{1}{8} a^{3} + \frac{17}{8} a + \frac{1}{2}\) , \( -\frac{573}{4} a^{3} + 290 a^{2} + \frac{6661}{4} a - 3371\) , \( \frac{16645}{4} a^{3} - \frac{12851}{2} a^{2} - \frac{193463}{4} a + 74676\bigr] \)
|
Rank: \( 1 \)
\(\left(\begin{array}{rrrr}
1 & 2 & 4 & 4 \\
2 & 1 & 2 & 2 \\
4 & 2 & 1 & 4 \\
4 & 2 & 4 & 1
\end{array}\right)\)
