Elliptic curves in class 10.1-c over 4.4.6809.1
Isogeny class 10.1-c contains
8 curves linked by isogenies of
degrees dividing 16.
| Curve label |
Weierstrass Coefficients |
| 10.1-c1
| \( \bigl[a^{2} + a - 3\) , \( a^{2} - a - 3\) , \( a^{3} + a^{2} - 4 a - 3\) , \( -3313 a^{3} - 316 a^{2} + 11602 a - 4042\) , \( -177734 a^{3} - 19498 a^{2} + 618172 a - 212855\bigr] \)
|
| 10.1-c2
| \( \bigl[a^{2} - 2\) , \( -a^{3} - a^{2} + 5 a + 4\) , \( a\) , \( -15 a^{3} + 4 a^{2} + 71 a - 9\) , \( 20 a^{3} - 14 a^{2} - 95 a + 50\bigr] \)
|
| 10.1-c3
| \( \bigl[1\) , \( a^{2} + a - 2\) , \( a^{2} - 3\) , \( 2 a^{2} - a + 2\) , \( 2 a^{2} - a - 2\bigr] \)
|
| 10.1-c4
| \( \bigl[1\) , \( -a^{2} + a + 2\) , \( a^{2} + a - 2\) , \( -342 a^{3} - 944 a^{2} - 436 a - 3\) , \( -15444 a^{3} - 36457 a^{2} - 6453 a + 5559\bigr] \)
|
| 10.1-c5
| \( \bigl[1\) , \( -a^{2} + a + 2\) , \( a^{2} + a - 2\) , \( -22 a^{3} - 59 a^{2} - 26 a + 2\) , \( -235 a^{3} - 558 a^{2} - 111 a + 77\bigr] \)
|
| 10.1-c6
| \( \bigl[1\) , \( -a^{2} + a + 2\) , \( a^{2} + a - 2\) , \( -2 a^{3} - 4 a^{2} - a + 2\) , \( -3 a^{3} - 7 a^{2} - a\bigr] \)
|
| 10.1-c7
| \( \bigl[1\) , \( -a^{2} + a + 2\) , \( a^{2} + a - 2\) , \( -22 a^{3} - 54 a^{2} - 16 a + 7\) , \( -274 a^{3} - 663 a^{2} - 149 a + 83\bigr] \)
|
| 10.1-c8
| \( \bigl[1\) , \( -a^{2} + a + 2\) , \( a^{2} + a - 2\) , \( -6602 a^{3} - 15244 a^{2} - 1911 a + 2702\) , \( -1026911 a^{3} - 2353003 a^{2} - 255035 a + 447068\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrrrrrr}
1 & 16 & 16 & 2 & 4 & 8 & 8 & 4 \\
16 & 1 & 4 & 8 & 4 & 2 & 8 & 16 \\
16 & 4 & 1 & 8 & 4 & 2 & 8 & 16 \\
2 & 8 & 8 & 1 & 2 & 4 & 4 & 2 \\
4 & 4 & 4 & 2 & 1 & 2 & 2 & 4 \\
8 & 2 & 2 & 4 & 2 & 1 & 4 & 8 \\
8 & 8 & 8 & 4 & 2 & 4 & 1 & 8 \\
4 & 16 & 16 & 2 & 4 & 8 & 8 & 1
\end{array}\right)\)
