Elliptic curves in class 10.1-f over 4.4.13676.1
Isogeny class 10.1-f contains
6 curves linked by isogenies of
degrees dividing 8.
| Curve label |
Weierstrass Coefficients |
| 10.1-f1
| \( \bigl[a^{2} - 2\) , \( -a^{3} + 4 a - 2\) , \( a^{3} - 5 a + 3\) , \( -4 a^{3} + 4 a^{2} + 21 a - 26\) , \( 6 a^{3} - 7 a^{2} - 36 a + 48\bigr] \)
|
| 10.1-f2
| \( \bigl[a^{3} + a^{2} - 4 a - 1\) , \( a - 1\) , \( a^{3} - 5 a + 2\) , \( -159 a^{3} + 550 a^{2} - 419 a - 62\) , \( -6046 a^{3} + 21059 a^{2} - 16030 a - 2459\bigr] \)
|
| 10.1-f3
| \( \bigl[a^{3} + a^{2} - 4 a - 1\) , \( a^{3} - 5 a + 1\) , \( a^{3} + a^{2} - 5 a\) , \( 166 a^{3} + 72 a^{2} - 900 a - 116\) , \( 1653 a^{3} + 686 a^{2} - 8872 a - 1152\bigr] \)
|
| 10.1-f4
| \( \bigl[1\) , \( 1\) , \( a^{3} + a^{2} - 5 a\) , \( -8 a^{3} - 10 a^{2} + 29 a + 4\) , \( 236 a^{3} + 278 a^{2} - 805 a - 108\bigr] \)
|
| 10.1-f5
| \( \bigl[a^{3} - 4 a + 2\) , \( a^{3} + a^{2} - 6 a - 2\) , \( a^{3} - 5 a + 2\) , \( 116 a^{3} + 51 a^{2} - 625 a - 85\) , \( -869 a^{3} - 373 a^{2} + 4681 a + 606\bigr] \)
|
| 10.1-f6
| \( \bigl[a^{3} - 5 a + 3\) , \( -a^{2} - a + 3\) , \( 1\) , \( -2 a^{3} + 6 a^{2} + 13 a - 36\) , \( -24 a^{3} + 32 a^{2} + 142 a - 213\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrrrr}
1 & 4 & 8 & 8 & 2 & 4 \\
4 & 1 & 8 & 8 & 2 & 4 \\
8 & 8 & 1 & 4 & 4 & 2 \\
8 & 8 & 4 & 1 & 4 & 2 \\
2 & 2 & 4 & 4 & 1 & 2 \\
4 & 4 & 2 & 2 & 2 & 1
\end{array}\right)\)
