Elliptic curves in class 242.1-i over 4.4.2777.1
Isogeny class 242.1-i contains
6 curves linked by isogenies of
degrees dividing 8.
| Curve label |
Weierstrass Coefficients |
| 242.1-i1
| \( \bigl[a^{3} - 4 a - 1\) , \( a^{2} - 2\) , \( a^{2} - a - 2\) , \( -291 a^{3} + 507 a^{2} + 824 a - 932\) , \( 4132 a^{3} - 6993 a^{2} - 11746 a + 12304\bigr] \)
|
| 242.1-i2
| \( \bigl[a^{2} - a - 1\) , \( -a^{3} + a^{2} + 4 a\) , \( a^{2} - 2\) , \( 4 a^{3} - 20 a^{2} + 2 a + 13\) , \( 5 a^{3} - 42 a^{2} + 4 a + 23\bigr] \)
|
| 242.1-i3
| \( \bigl[a^{2} - 1\) , \( a^{3} - a^{2} - 3 a + 1\) , \( 1\) , \( 2 a^{3} - a^{2} - 5 a + 1\) , \( 8 a^{3} - 2 a^{2} - 31 a - 15\bigr] \)
|
| 242.1-i4
| \( \bigl[a^{2} - 1\) , \( -a^{2} + 2 a + 1\) , \( a + 1\) , \( 12 a^{3} - 37 a^{2} + 8 a + 11\) , \( 59 a^{3} - 156 a^{2} - 31 a + 97\bigr] \)
|
| 242.1-i5
| \( \bigl[a^{2} - 1\) , \( -a^{2} + 2 a + 1\) , \( a + 1\) , \( 257 a^{3} - 722 a^{2} - 27 a + 381\) , \( 4461 a^{3} - 11797 a^{2} - 888 a + 6275\bigr] \)
|
| 242.1-i6
| \( \bigl[a + 1\) , \( -a^{3} + 2 a^{2} + 2 a - 4\) , \( 0\) , \( 19 a^{3} + 19 a^{2} - 49 a - 52\) , \( -227 a^{3} - 362 a^{2} + 54 a + 126\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrrrr}
1 & 4 & 8 & 2 & 4 & 8 \\
4 & 1 & 2 & 2 & 4 & 2 \\
8 & 2 & 1 & 4 & 8 & 4 \\
2 & 2 & 4 & 1 & 2 & 4 \\
4 & 4 & 8 & 2 & 1 & 8 \\
8 & 2 & 4 & 4 & 8 & 1
\end{array}\right)\)
