Isogeny class 17.2-a contains
4 curves linked by isogenies of
degrees dividing 10.
| Curve label |
Weierstrass Coefficients |
| 17.2-a1
| \( \bigl[-\frac{1}{5} a^{3} + \frac{4}{5} a^{2} + \frac{11}{5} a - \frac{12}{5}\) , \( \frac{1}{5} a^{3} + \frac{1}{5} a^{2} - \frac{11}{5} a - \frac{13}{5}\) , \( 1\) , \( \frac{19}{5} a^{3} - \frac{121}{5} a^{2} + \frac{156}{5} a - \frac{32}{5}\) , \( \frac{163}{5} a^{3} - \frac{1032}{5} a^{2} + \frac{832}{5} a - \frac{44}{5}\bigr] \)
|
| 17.2-a2
| \( \bigl[-\frac{1}{5} a^{3} + \frac{4}{5} a^{2} + \frac{11}{5} a - \frac{12}{5}\) , \( \frac{1}{5} a^{3} + \frac{1}{5} a^{2} - \frac{11}{5} a - \frac{13}{5}\) , \( 1\) , \( -\frac{1}{5} a^{3} + \frac{9}{5} a^{2} + \frac{51}{5} a - \frac{22}{5}\) , \( \frac{16}{5} a^{3} - \frac{29}{5} a^{2} - \frac{51}{5} a + \frac{42}{5}\bigr] \)
|
| 17.2-a3
| \( \bigl[-\frac{1}{5} a^{3} + \frac{4}{5} a^{2} + \frac{11}{5} a - \frac{12}{5}\) , \( -1\) , \( -\frac{1}{5} a^{3} + \frac{4}{5} a^{2} + \frac{6}{5} a - \frac{17}{5}\) , \( \frac{56}{5} a^{3} - \frac{99}{5} a^{2} - \frac{496}{5} a + \frac{462}{5}\) , \( -\frac{549}{5} a^{3} + \frac{1046}{5} a^{2} + \frac{5069}{5} a - \frac{4938}{5}\bigr] \)
|
| 17.2-a4
| \( \bigl[1\) , \( -\frac{1}{5} a^{3} + \frac{4}{5} a^{2} + \frac{11}{5} a - \frac{22}{5}\) , \( -\frac{1}{5} a^{3} + \frac{4}{5} a^{2} + \frac{6}{5} a - \frac{17}{5}\) , \( \frac{6}{5} a^{3} - \frac{14}{5} a^{2} - \frac{31}{5} a + \frac{37}{5}\) , \( -a^{3} + 5 a^{2} + a - 5\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrr}
1 & 2 & 5 & 10 \\
2 & 1 & 10 & 5 \\
5 & 10 & 1 & 2 \\
10 & 5 & 2 & 1
\end{array}\right)\)
