Rank: \( 0 \)
\(\left(\begin{array}{rrrr}
1 & 2 & 4 & 4 \\
2 & 1 & 2 & 2 \\
4 & 2 & 1 & 4 \\
4 & 2 & 4 & 1
\end{array}\right)\)
Elliptic curves in class 8.2-a over 4.4.7232.1
Isogeny class 8.2-a contains
4 curves linked by isogenies of
degrees dividing 4.
| Curve label |
Weierstrass Coefficients |
| 8.2-a1
| \( \bigl[\frac{1}{2} a^{3} - \frac{3}{2} a - 2\) , \( -\frac{1}{2} a^{3} + \frac{5}{2} a + 2\) , \( a + 1\) , \( \frac{551}{2} a^{3} - 213 a^{2} - \frac{3273}{2} a - 902\) , \( \frac{12291}{2} a^{3} - 4778 a^{2} - \frac{73129}{2} a - 20110\bigr] \)
|
| 8.2-a2
| \( \bigl[\frac{1}{2} a^{3} - \frac{3}{2} a - 2\) , \( -\frac{1}{2} a^{3} + \frac{5}{2} a + 2\) , \( a + 1\) , \( 18 a^{3} - 13 a^{2} - 104 a - 57\) , \( \frac{219}{2} a^{3} - 83 a^{2} - \frac{1293}{2} a - 356\bigr] \)
|
| 8.2-a3
| \( \bigl[\frac{1}{2} a^{3} - \frac{3}{2} a - 2\) , \( -a^{2} + a + 3\) , \( \frac{1}{2} a^{3} - a^{2} - \frac{1}{2} a + 2\) , \( a^{3} + 3\) , \( -13 a^{3} - 14 a^{2} + 23 a + 17\bigr] \)
|
| 8.2-a4
| \( \bigl[\frac{1}{2} a^{3} - a^{2} - \frac{1}{2} a + 2\) , \( \frac{1}{2} a^{3} - \frac{7}{2} a - 3\) , \( 0\) , \( -3 a^{3} + 3 a^{2} + 25 a + 4\) , \( \frac{27}{2} a^{3} - 19 a^{2} - \frac{113}{2} a - 17\bigr] \)
|
