Elliptic curves in class 33.1-f over 4.4.4752.1
Isogeny class 33.1-f contains
8 curves linked by isogenies of
degrees dividing 16.
Curve label |
Weierstrass Coefficients |
33.1-f1
| \( \bigl[a^{2} - a - 2\) , \( -a^{2} + a + 1\) , \( 0\) , \( 335 a^{2} - 335 a - 1279\) , \( 4719 a^{2} - 4719 a - 17652\bigr] \)
|
33.1-f2
| \( \bigl[a^{2} - a - 2\) , \( -a^{2} + a + 1\) , \( 0\) , \( 40 a^{3} - 240 a^{2} + 370 a - 134\) , \( -1216 a^{3} + 4596 a^{2} - 3810 a + 141\bigr] \)
|
33.1-f3
| \( \bigl[a^{2} - a - 2\) , \( -a^{2} + a + 1\) , \( 0\) , \( 25 a^{2} - 25 a - 79\) , \( 89 a^{2} - 89 a - 316\bigr] \)
|
33.1-f4
| \( \bigl[a^{2} - a - 2\) , \( -a^{2} + a + 1\) , \( 0\) , \( 20 a^{2} - 20 a - 79\) , \( 84 a^{2} - 84 a - 306\bigr] \)
|
33.1-f5
| \( \bigl[a^{2} - a - 2\) , \( -a^{2} + a + 1\) , \( 0\) , \( -20 a^{2} + 20 a - 9\) , \( 100 a^{2} - 100 a - 16\bigr] \)
|
33.1-f6
| \( \bigl[a^{2} - a - 2\) , \( -a^{2} + a + 1\) , \( 0\) , \( -4\) , \( 4 a^{2} - 4 a - 7\bigr] \)
|
33.1-f7
| \( \bigl[a^{2} - a - 2\) , \( -a^{2} + a + 1\) , \( 0\) , \( 1\) , \( 0\bigr] \)
|
33.1-f8
| \( \bigl[a^{2} - a - 2\) , \( -a^{2} + a + 1\) , \( 0\) , \( -40 a^{3} - 120 a^{2} - 10 a + 36\) , \( 1216 a^{3} + 948 a^{2} - 1734 a - 289\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrrrrrr}
1 & 16 & 4 & 2 & 8 & 4 & 8 & 16 \\
16 & 1 & 16 & 8 & 2 & 4 & 8 & 4 \\
4 & 16 & 1 & 2 & 8 & 4 & 8 & 16 \\
2 & 8 & 2 & 1 & 4 & 2 & 4 & 8 \\
8 & 2 & 8 & 4 & 1 & 2 & 4 & 2 \\
4 & 4 & 4 & 2 & 2 & 1 & 2 & 4 \\
8 & 8 & 8 & 4 & 4 & 2 & 1 & 8 \\
16 & 4 & 16 & 8 & 2 & 4 & 8 & 1
\end{array}\right)\)