Elliptic curves in class 10.1-a over 4.4.16609.1
Isogeny class 10.1-a contains
4 curves linked by isogenies of
degrees dividing 4.
| Curve label |
Weierstrass Coefficients |
| 10.1-a1
| \( \bigl[a^{2} - 4\) , \( a^{3} - a^{2} - 5 a + 2\) , \( a^{3} - 3 a\) , \( a^{3} - 2 a^{2} - 6 a + 7\) , \( -2 a^{2} - 2 a + 4\bigr] \)
|
| 10.1-a2
| \( \bigl[a^{2} + a - 3\) , \( a^{2} - a - 3\) , \( a^{3} - 4 a - 1\) , \( 571 a^{3} + 673 a^{2} - 3201 a - 4346\) , \( -17894 a^{3} - 21137 a^{2} + 100288 a + 136346\bigr] \)
|
| 10.1-a3
| \( \bigl[a^{2} + a - 3\) , \( a^{2} - a - 3\) , \( a^{3} - 4 a - 1\) , \( 36 a^{3} + 43 a^{2} - 201 a - 271\) , \( -303 a^{3} - 357 a^{2} + 1700 a + 2309\bigr] \)
|
| 10.1-a4
| \( \bigl[a^{2} + a - 3\) , \( a^{3} - 4 a\) , \( a^{3} - a^{2} - 3 a + 3\) , \( 18 a^{3} - 23 a^{2} - 75 a + 94\) , \( 45 a^{3} - 57 a^{2} - 208 a + 250\bigr] \)
|
Rank: \( 1 \)
\(\left(\begin{array}{rrrr}
1 & 4 & 2 & 4 \\
4 & 1 & 2 & 4 \\
2 & 2 & 1 & 2 \\
4 & 4 & 2 & 1
\end{array}\right)\)
