Elliptic curves in class 10.1-d over 4.4.13676.1
Isogeny class 10.1-d contains
8 curves linked by isogenies of
degrees dividing 16.
| Curve label |
Weierstrass Coefficients |
| 10.1-d1
| \( \bigl[a^{2} - 2\) , \( -a^{3} + a^{2} + 4 a - 6\) , \( a^{3} - 4 a + 3\) , \( -1058 a^{3} + 867 a^{2} + 6709 a - 8273\) , \( -36079 a^{3} + 34756 a^{2} + 227338 a - 290618\bigr] \)
|
| 10.1-d2
| \( \bigl[a^{2} - 2\) , \( -a^{3} + a^{2} + 4 a - 6\) , \( a^{3} - 4 a + 3\) , \( 7 a^{3} - 203 a^{2} + 614 a - 483\) , \( 1556 a^{3} - 6577 a^{2} + 8225 a - 2863\bigr] \)
|
| 10.1-d3
| \( \bigl[a^{2} - 2\) , \( -a^{3} + a^{2} + 4 a - 6\) , \( a^{3} - 4 a + 3\) , \( -8 a^{3} - 3 a^{2} + 79 a - 83\) , \( 103 a^{3} - 220 a^{2} - 236 a + 486\bigr] \)
|
| 10.1-d4
| \( \bigl[a^{2} - 2\) , \( -a^{3} + a^{2} + 4 a - 6\) , \( a^{3} - 4 a + 3\) , \( -34 a^{3} - 15 a^{2} + 172 a + 36\) , \( -40 a^{3} - 15 a^{2} + 203 a + 17\bigr] \)
|
| 10.1-d5
| \( \bigl[a\) , \( -a^{2} + 3\) , \( a^{3} + a^{2} - 4 a\) , \( -3362 a^{3} - 4000 a^{2} + 11495 a + 1565\) , \( -214234 a^{3} - 253576 a^{2} + 731826 a + 97924\bigr] \)
|
| 10.1-d6
| \( \bigl[1\) , \( -1\) , \( a^{3} - 4 a + 2\) , \( 79 a^{3} + 26 a^{2} - 449 a - 60\) , \( -695 a^{3} - 266 a^{2} + 3832 a + 496\bigr] \)
|
| 10.1-d7
| \( \bigl[1\) , \( -1\) , \( a^{3} - 4 a + 2\) , \( 4 a^{3} + a^{2} - 24 a - 5\) , \( -13 a^{3} - 6 a^{2} + 70 a + 8\bigr] \)
|
| 10.1-d8
| \( \bigl[a^{3} - 5 a + 3\) , \( a^{3} + a^{2} - 5 a\) , \( a^{3} - 4 a + 2\) , \( 803 a^{3} + 358 a^{2} - 4292 a - 557\) , \( -45114 a^{3} - 19366 a^{2} + 243016 a + 31563\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrrrrrr}
1 & 2 & 4 & 8 & 4 & 16 & 8 & 16 \\
2 & 1 & 2 & 4 & 2 & 8 & 4 & 8 \\
4 & 2 & 1 & 2 & 4 & 4 & 2 & 4 \\
8 & 4 & 2 & 1 & 8 & 8 & 4 & 8 \\
4 & 2 & 4 & 8 & 1 & 16 & 8 & 16 \\
16 & 8 & 4 & 8 & 16 & 1 & 2 & 4 \\
8 & 4 & 2 & 4 & 8 & 2 & 1 & 2 \\
16 & 8 & 4 & 8 & 16 & 4 & 2 & 1
\end{array}\right)\)
