Elliptic curves in class 68.1-a over 4.4.2624.1
Isogeny class 68.1-a contains
4 curves linked by isogenies of
degrees dividing 10.
| Curve label |
Weierstrass Coefficients |
| 68.1-a1
| \( \bigl[a^{3} - a^{2} - 3 a + 1\) , \( a^{2} - a\) , \( a^{3} - 2 a^{2} - a + 1\) , \( 42 a^{3} + 135 a^{2} - 925 a - 1700\) , \( 1425 a^{3} - 133 a^{2} - 21240 a - 27307\bigr] \)
|
| 68.1-a2
| \( \bigl[a^{3} - a^{2} - 3 a + 1\) , \( a^{2} - a\) , \( a^{3} - 2 a^{2} - a + 1\) , \( -398 a^{3} + 955 a^{2} + 815 a - 1200\) , \( -6011 a^{3} + 14251 a^{2} + 12512 a - 17359\bigr] \)
|
| 68.1-a3
| \( \bigl[a^{3} - a^{2} - 3 a + 1\) , \( a^{2} - a\) , \( a^{3} - 2 a^{2} - a + 1\) , \( 17 a^{3} - 10 a^{2} - 70 a - 35\) , \( -59 a^{3} + 74 a^{2} + 252 a + 87\bigr] \)
|
| 68.1-a4
| \( \bigl[a^{3} - a^{2} - 3 a + 1\) , \( a^{2} - a\) , \( a^{3} - 2 a^{2} - a + 1\) , \( 2 a^{3} + 5 a^{2} - 5 a - 5\) , \( 3 a^{3} + 7 a^{2} + 3 a - 2\bigr] \)
|
Rank: \( 1 \)
\(\left(\begin{array}{rrrr}
1 & 2 & 5 & 10 \\
2 & 1 & 10 & 5 \\
5 & 10 & 1 & 2 \\
10 & 5 & 2 & 1
\end{array}\right)\)
