Elliptic curves in class 16.1-b over 4.4.4913.1
Isogeny class 16.1-b contains
12 curves linked by isogenies of
degrees dividing 24.
| Curve label |
Weierstrass Coefficients |
| 16.1-b1
| \( \bigl[-\frac{1}{2} a^{3} + a^{2} + 3 a - \frac{3}{2}\) , \( 0\) , \( 1\) , \( -\frac{13}{2} a^{3} + 4 a^{2} + 21 a - \frac{21}{2}\) , \( -10 a^{3} - 29 a^{2} + 57 a - 20\bigr] \)
|
| 16.1-b2
| \( \bigl[-\frac{1}{2} a^{3} + a^{2} + 3 a - \frac{3}{2}\) , \( 0\) , \( 1\) , \( a^{3} - a^{2} - 4 a + 2\) , \( a^{2} - a\bigr] \)
|
| 16.1-b3
| \( \bigl[-\frac{1}{2} a^{3} + a^{2} + 3 a - \frac{3}{2}\) , \( -\frac{1}{2} a^{3} + 3 a + \frac{3}{2}\) , \( \frac{1}{2} a^{3} - 2 a - \frac{1}{2}\) , \( 49 a^{3} - 295 a^{2} + 229 a - 46\) , \( \frac{4121}{2} a^{3} - 5454 a^{2} - 245 a + \frac{2353}{2}\bigr] \)
|
| 16.1-b4
| \( \bigl[-\frac{1}{2} a^{3} + a^{2} + 3 a - \frac{3}{2}\) , \( -\frac{1}{2} a^{3} + 3 a + \frac{3}{2}\) , \( \frac{1}{2} a^{3} - 2 a - \frac{1}{2}\) , \( -11 a^{3} - 15 a^{2} + 69 a - 26\) , \( -\frac{79}{2} a^{3} - 94 a^{2} + 227 a - \frac{167}{2}\bigr] \)
|
| 16.1-b5
| \( \bigl[-\frac{1}{2} a^{3} + a^{2} + 3 a - \frac{1}{2}\) , \( -a^{3} + a^{2} + 6 a\) , \( a + 1\) , \( \frac{527}{2} a^{3} - 135 a^{2} - 1646 a - \frac{1075}{2}\) , \( 4245 a^{3} - 2173 a^{2} - 26530 a - 8703\bigr] \)
|
| 16.1-b6
| \( \bigl[-\frac{1}{2} a^{3} + a^{2} + 3 a - \frac{1}{2}\) , \( -a^{3} + a^{2} + 6 a\) , \( a + 1\) , \( -19 a^{3} + 10 a^{2} + 119 a + 40\) , \( -17 a^{3} + 9 a^{2} + 107 a + 35\bigr] \)
|
| 16.1-b7
| \( \bigl[-\frac{1}{2} a^{3} + a^{2} + 3 a - \frac{1}{2}\) , \( -a^{2} + 2 a + 3\) , \( a + 1\) , \( 2251 a^{3} - 1133 a^{2} - 14091 a - 4744\) , \( -\frac{143863}{2} a^{3} + 36944 a^{2} + 449440 a + \frac{293461}{2}\bigr] \)
|
| 16.1-b8
| \( \bigl[-\frac{1}{2} a^{3} + a^{2} + 3 a - \frac{1}{2}\) , \( -a^{2} + 2 a + 3\) , \( a + 1\) , \( 731 a^{3} - 373 a^{2} - 4571 a - 1504\) , \( \frac{34473}{2} a^{3} - 8824 a^{2} - 107728 a - \frac{70683}{2}\bigr] \)
|
| 16.1-b9
| \( \bigl[1\) , \( -a^{3} + a^{2} + 5 a\) , \( a^{2} - a - 2\) , \( -\frac{23}{2} a^{3} + 11 a^{2} + 58 a - \frac{61}{2}\) , \( -\frac{55}{2} a^{3} + 27 a^{2} + 138 a - \frac{143}{2}\bigr] \)
|
| 16.1-b10
| \( \bigl[1\) , \( -a^{3} + a^{2} + 5 a\) , \( a^{2} - a - 2\) , \( -\frac{3}{2} a^{3} + a^{2} + 8 a - \frac{1}{2}\) , \( \frac{1}{2} a^{3} - a^{2} - 2 a + \frac{1}{2}\bigr] \)
|
| 16.1-b11
| \( \bigl[1\) , \( a^{3} - a^{2} - 5 a + 1\) , \( a^{2} - a - 3\) , \( \frac{23}{2} a^{3} - 12 a^{2} - 57 a - \frac{37}{2}\) , \( 28 a^{3} - 28 a^{2} - 140 a - 45\bigr] \)
|
| 16.1-b12
| \( \bigl[1\) , \( a^{3} - a^{2} - 5 a + 1\) , \( a^{2} - a - 3\) , \( \frac{3}{2} a^{3} - 2 a^{2} - 7 a + \frac{3}{2}\) , \( -1\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrrrrrrrrrr}
1 & 3 & 8 & 4 & 8 & 24 & 4 & 2 & 12 & 6 & 24 & 12 \\
3 & 1 & 24 & 12 & 24 & 8 & 12 & 6 & 4 & 2 & 8 & 4 \\
8 & 24 & 1 & 2 & 4 & 12 & 8 & 4 & 24 & 12 & 3 & 6 \\
4 & 12 & 2 & 1 & 2 & 6 & 4 & 2 & 12 & 6 & 6 & 3 \\
8 & 24 & 4 & 2 & 1 & 3 & 8 & 4 & 24 & 12 & 12 & 6 \\
24 & 8 & 12 & 6 & 3 & 1 & 24 & 12 & 8 & 4 & 4 & 2 \\
4 & 12 & 8 & 4 & 8 & 24 & 1 & 2 & 3 & 6 & 24 & 12 \\
2 & 6 & 4 & 2 & 4 & 12 & 2 & 1 & 6 & 3 & 12 & 6 \\
12 & 4 & 24 & 12 & 24 & 8 & 3 & 6 & 1 & 2 & 8 & 4 \\
6 & 2 & 12 & 6 & 12 & 4 & 6 & 3 & 2 & 1 & 4 & 2 \\
24 & 8 & 3 & 6 & 12 & 4 & 24 & 12 & 8 & 4 & 1 & 2 \\
12 & 4 & 6 & 3 & 6 & 2 & 12 & 6 & 4 & 2 & 2 & 1
\end{array}\right)\)
