Elliptic curves in class 21.1-c over 4.4.9909.1
Isogeny class 21.1-c contains
4 curves linked by isogenies of
degrees dividing 4.
| Curve label |
Weierstrass Coefficients |
| 21.1-c1
| \( \bigl[a\) , \( a^{2} - a - 4\) , \( a^{3} - 5 a - 2\) , \( 247 a^{3} - 369 a^{2} - 783 a + 29\) , \( -2748 a^{3} + 5314 a^{2} + 6231 a - 5064\bigr] \)
|
| 21.1-c2
| \( \bigl[a^{3} - a^{2} - 4 a + 1\) , \( a^{3} - a^{2} - 4 a + 1\) , \( a + 1\) , \( 203 a^{3} + 99 a^{2} - 1170 a - 1195\) , \( -3273 a^{3} - 1665 a^{2} + 18781 a + 19343\bigr] \)
|
| 21.1-c3
| \( \bigl[a^{3} - a^{2} - 4 a + 1\) , \( a^{3} - a^{2} - 4 a + 1\) , \( a + 1\) , \( 3 a^{3} - a^{2} - 15 a - 5\) , \( -135 a^{3} - 70 a^{2} + 775 a + 803\bigr] \)
|
| 21.1-c4
| \( \bigl[a + 1\) , \( a^{3} - 4 a - 2\) , \( a^{2} - 2\) , \( -167 a^{3} - 178 a^{2} + 229 a - 60\) , \( 1329 a^{3} + 5176 a^{2} + 3359 a - 3168\bigr] \)
|
Rank not yet determined.
\(\left(\begin{array}{rrrr}
1 & 2 & 4 & 4 \\
2 & 1 & 2 & 2 \\
4 & 2 & 1 & 4 \\
4 & 2 & 4 & 1
\end{array}\right)\)
