Elliptic curves in class 4.1-c over 4.4.10512.1
Isogeny class 4.1-c contains
6 curves linked by isogenies of
degrees dividing 45.
| Curve label |
Weierstrass Coefficients |
| 4.1-c1
| \( \bigl[a^{3} - 5 a - 5\) , \( a^{3} - 2 a^{2} - 3 a + 4\) , \( a^{3} - a^{2} - 4 a\) , \( 37 a^{3} - 35 a^{2} - 174 a - 89\) , \( 49 a^{3} - 134 a^{2} - 66 a + 221\bigr] \)
|
| 4.1-c2
| \( \bigl[a^{3} - 5 a - 4\) , \( a^{2} - 2 a - 5\) , \( a^{2} - 4\) , \( 46 a^{3} - 47 a^{2} - 223 a - 106\) , \( -36 a^{3} + 215 a^{2} - 110 a - 571\bigr] \)
|
| 4.1-c3
| \( \bigl[a^{3} - 5 a - 4\) , \( a^{2} - 2 a - 5\) , \( a^{2} - 4\) , \( a^{3} + 3 a^{2} - 3 a - 11\) , \( a^{3} + 4 a^{2} + 3 a - 5\bigr] \)
|
| 4.1-c4
| \( \bigl[a^{3} - a^{2} - 4 a - 1\) , \( a - 1\) , \( 1\) , \( 1949 a^{3} - 2435 a^{2} - 10586 a + 1554\) , \( 48278 a^{3} - 60389 a^{2} - 262368 a + 38590\bigr] \)
|
| 4.1-c5
| \( \bigl[1\) , \( -a + 1\) , \( a^{3} - a^{2} - 5 a - 1\) , \( 2253 a^{3} - 4398 a^{2} - 7394 a + 1117\) , \( -114542 a^{3} + 212243 a^{2} + 407642 a - 62220\bigr] \)
|
| 4.1-c6
| \( \bigl[1\) , \( -a^{3} + a^{2} + 6 a + 2\) , \( a^{3} - a^{2} - 5 a - 1\) , \( 1834 a^{3} + 311 a^{2} - 13041 a - 13479\) , \( -84208 a^{3} - 13493 a^{2} + 586108 a + 591353\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrrrr}
1 & 9 & 3 & 15 & 5 & 45 \\
9 & 1 & 3 & 15 & 45 & 5 \\
3 & 3 & 1 & 5 & 15 & 15 \\
15 & 15 & 5 & 1 & 3 & 3 \\
5 & 45 & 15 & 3 & 1 & 9 \\
45 & 5 & 15 & 3 & 9 & 1
\end{array}\right)\)
