Elliptic curves in class 16.2-a over 4.4.13068.1
Isogeny class 16.2-a contains
6 curves linked by isogenies of
degrees dividing 99.
| Curve label |
Weierstrass Coefficients |
| 16.2-a1
| \( \bigl[0\) , \( -2 a^{3} + 3 a^{2} + 9 a - 2\) , \( a^{3} - a^{2} - 5 a - 1\) , \( -71 a^{3} + 325 a^{2} - 353 a + 69\) , \( 1083 a^{3} - 2934 a^{2} - 1329 a + 685\bigr] \)
|
| 16.2-a2
| \( \bigl[0\) , \( -a^{3} + 2 a^{2} + 5 a - 1\) , \( a^{3} - a^{2} - 5 a - 1\) , \( 76 a^{3} - 51 a^{2} - 472 a - 228\) , \( -564 a^{3} + 379 a^{2} + 3508 a + 1715\bigr] \)
|
| 16.2-a3
| \( \bigl[0\) , \( -a^{2} + a + 2\) , \( a^{3} - a^{2} - 5 a - 1\) , \( 15 a^{3} - 9 a^{2} - 95 a - 49\) , \( 70 a^{3} - 47 a^{2} - 434 a - 212\bigr] \)
|
| 16.2-a4
| \( \bigl[0\) , \( -a^{3} + 2 a^{2} + 5 a - 1\) , \( a^{3} - a^{2} - 5 a - 1\) , \( -344 a^{3} + 229 a^{2} + 2148 a + 1052\) , \( -2313 a^{3} + 1556 a^{2} + 14383 a + 7036\bigr] \)
|
| 16.2-a5
| \( \bigl[0\) , \( -a^{2} + a + 2\) , \( a^{3} - a^{2} - 5 a - 1\) , \( -125 a^{3} + 131 a^{2} + 725 a + 131\) , \( 429 a^{3} - 522 a^{2} - 2387 a - 15\bigr] \)
|
| 16.2-a6
| \( \bigl[0\) , \( -a\) , \( a^{3} - a^{2} - 5 a - 1\) , \( 6116 a^{3} - 9465 a^{2} - 31516 a + 11156\) , \( -145256 a^{3} + 224894 a^{2} + 748229 a - 264949\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrrrr}
1 & 33 & 3 & 11 & 9 & 99 \\
33 & 1 & 11 & 3 & 33 & 3 \\
3 & 11 & 1 & 33 & 3 & 33 \\
11 & 3 & 33 & 1 & 99 & 9 \\
9 & 33 & 3 & 99 & 1 & 11 \\
99 & 3 & 33 & 9 & 11 & 1
\end{array}\right)\)
